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  • simulation  (107)
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  • Mathematics  (126)
  • Mechanical Engineering, Materials Science, Production Engineering, Mining and Metallurgy, Traffic Engineering, Precision Mechanics  (38)
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  • Articles  (174)
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  • 1
    Electronic Resource
    Electronic Resource
    Springer
    The journal of Fourier analysis and applications 4 (1998), S. 199-214 
    ISSN: 1531-5851
    Keywords: Primary 33E20 ; 41A15 ; 41A30 ; secondary 47D25 ; Wavelets ; multiresolution analysis ; unitary operators ; low-pass filters ; wandering vectors ; QMF ; scaling functions
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Abstract This article provides classes of unitary operators of L2(R) contained in the commutant of the Shift operator, such that for any pair of multiresolution analyses of L2(R) there exists a unitary operator in one of these classes, which maps all the scaling functions of the first multiresolution analysis to scaling functions of the other. We use these unitary operators to provide an interesting class of scaling functions. We show that the Dai-Larson unitary parametrization of orthonormal wavelets is not suitable for the study of scaling functions. These operators give an interesting relation between low-pass filters corresponding to scaling functions, which is implemented by a special class of unitary operators acting on L2([−π, π)), which we characterize. Using this characterization we recapture Daubechies' orthonormal wavelets bypassing the spectral factorization process.
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  • 2
    Electronic Resource
    Electronic Resource
    Springer
    OR spectrum 19 (1997), S. 23-29 
    ISSN: 1436-6304
    Keywords: Job shop scheduling ; dispatching rules ; coordination ; look ahead information ; simulation ; Werkstattsteuerung ; Steuerungsregeln ; Koordination ; Vorausschauende Informationen ; Simulation
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics , Economics
    Description / Table of Contents: Zusammenfassung In diesem Beitrag wird ein neuartiger Ansatz zur Koordination dezentraler Werkstattsteuerungsregeln vorgestellt und mit Hilfe einer Simulationsstudie analysiert. Die Koordination basiert auf vorausschauenden Informationen und enthält einen Auftragsnachfrage-/-angebotsmechanismus. Die Simulations-experimente zeigen, daß durch den Einsatz des Koordinationsmechanismus die Leistung herkömmlicher Steuerungsregeln signifikant verbessert wird.
    Notes: Abstract In this paper a new coordination approach for decentralized job shop scheduling rules is presented and analyzed in a simulation study. The coordination is based on look ahead information and contains a mechanism for demanding and supplying jobs. The simulation experiments show that the performance of conventional scheduling rules is significantly improved using the coordination mechanism.
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  • 3
    Electronic Resource
    Electronic Resource
    Springer
    OR spectrum 19 (1997), S. 23-29 
    ISSN: 1436-6304
    Keywords: Key words: Job shop scheduling ; dispatching rules ; coordination ; look ahead information ; simulation ; Schlüsselwörter: Werkstattsteuerung ; Steuerungsregeln ; Koordination ; Vorausschauende Informationen ; Simulation
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics , Economics
    Description / Table of Contents: Zusammenfassung. In diesem Beitrag wird ein neu-artiger Ansatz zur Koordination dezentraler Werkstattsteuerungsregeln vorgestellt und mit Hilfe einer Simulationsstudie analysiert. Die Koordination basiert auf vorausschauenden Informationen und enthält einen Auftragsnachfrage-/-angebotsmechanismus. Die Simulations- experimente zeigen, daß durch den Einsatz des Koordinationsmechanismus die Leistung herkömmlicher Steuerungsregeln signifikant verbessert wird.
    Notes: Abstract. In this paper a new coordination approach for decentralized job shop scheduling rules is presented and analyzed in a simulation study. The coordination is based on look ahead information and contains a mechanism for demanding and supplying jobs. The simulation experiments show that the performance of conventional scheduling rules is significantly improved using the coordination mechanism.
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  • 4
    Electronic Resource
    Electronic Resource
    Springer
    Mathematical programming 42 (1988), S. 53-68 
    ISSN: 1436-4646
    Keywords: Design of experiments ; normal random variates ; pseudorandom ; simulation ; statistical inference
    Source: Springer Online Journal Archives 1860-2000
    Topics: Computer Science , Mathematics
    Notes: Abstract More and more problems are being tackled by simulation as large computing costs per hour approach those of mathematicians' time. Abuses of simulation arise from ignorance or careless use of little understood procedures, and some of the fundamental tools of the subject are much less well understood than commonly supposed. This is illustrated here by the saga of pseudorandom number generators, normal variate generators and the analysis of queueing system simulations. On the positive side, genuinely new uses of simulation are appearing, particularly in statistical inference. These are exemplified by recursive algorithms for simulating complex systems and simulation-based likelihood inference for point processes.
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  • 5
    Electronic Resource
    Electronic Resource
    Springer
    Journal of intelligent manufacturing 9 (1998), S. 225-234 
    ISSN: 1572-8145
    Keywords: Expert system ; advisory system ; machining ; simulation ; intelligent machining
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mechanical Engineering, Materials Science, Production Engineering, Mining and Metallurgy, Traffic Engineering, Precision Mechanics
    Notes: Abstract A unique advisory system is developed for machining processes. It is unique in using analytical and simulation models for the induction of rules, rules which must otherwise be generated from experiments. These rules are combined with heuristic rules for inferring optimal machining parameters. The utility and accuracy of the process models are illustrated and the architecture of the advisory system is described. Also described are its capability to incorporate other application programs through functions, regardless of the programming language, and to address constraints in decision making. Face milling is described as a specific application.
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  • 6
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    Journal of intelligent manufacturing 9 (1998), S. 361-367 
    ISSN: 1572-8145
    Keywords: Adaptive genetic algorithms ; flow-shop ; dynamic population size ; simulation
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mechanical Engineering, Materials Science, Production Engineering, Mining and Metallurgy, Traffic Engineering, Precision Mechanics
    Notes: Abstract This paper describes the characteristics of two hybrid genetic algorithms (GAs) for generating allocation and sequencing of production lots in a flow-shop environment based on a non-linear, multi-criteria objective function. Both GAs are used as search techniques: in the first model the task of the GA is to allocate and sequence the jobs; in the second model, the GA is combined with a dispatching rule (Earliest Due Date, EDD) thus limiting its task only on the allocation of the jobs. Both GAs are characterized by a dynamic population size with dynamic birth rate, as well as by multiple-operator reproduction criteria and by adaptive crossover and mutation rates. A discrete-event simulation model has been used in order to evaluate the performances of the tentative schedules. The proposed algorithms have been subsequently compared with a classical branch and bound method.
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  • 7
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    Journal of intelligent manufacturing 10 (1999), S. 323-329 
    ISSN: 1572-8145
    Keywords: Computer-aided design ; rapid prototyping ; modeling ; simulation
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mechanical Engineering, Materials Science, Production Engineering, Mining and Metallurgy, Traffic Engineering, Precision Mechanics
    Notes: Abstract The direct slicing of CAD models created in CADDS V to generate geometric data for rapid prototyping using fused feposition modeling technique (FDM) is presented in this paper. The report file from an explicit model is accessed for obtaining model data. Algorithms have been developed for determining the volumes of model material as well as support materials. New algorithms have been developed for filling the sheet solid. A simulation module has been developed to verify whether the filling is correctly done. Example of a model is manufactured using this approach is also presented in this paper.
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  • 8
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    Journal of intelligent manufacturing 10 (1999), S. 405-421 
    ISSN: 1572-8145
    Keywords: Flexible manufacturing systems control ; intelligent manufacturing ; neural networks ; simulation ; material handling systems ; automated guided vehicles
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mechanical Engineering, Materials Science, Production Engineering, Mining and Metallurgy, Traffic Engineering, Precision Mechanics
    Notes: Abstract This paper presents a framework of intelligent manufacturing scheduling and control with specific applications to operations of rail-guided vehicle systems (RGVS). A RGVS control architecture is discussed with a focus on a simulated experiment in operations of the load/unload area of a real industrial flexible manufacturing system (FMS). In the operation stage of a material handling system (MHS), all shop floor data are subject to change as time goes. These data can be collected using a data acquisition device and stored in a dynamic database. The RGVS simulator used in this experimental study is designed to incorporate some possible situations representing existing material handling scenarios in order to evaluate alternative control policies. At the development stage of the controller, all possible combinations of most commonly encountered scenarios such as RGV failures, production schedule changes, machine breakdowns, and rush orders are to be simulated and corresponding results collected. The data are then structured into training data pairs to properly train an artificial neural network. The neural network, trained by using input/output data sets obtained from a number of simulation runs, will then provide control strategy recommendations. At the application stage, whenever an abnormal scenario occurs, a pre-processor will be activated to pre-screen and prepare an input vector for the trained neural network. If such an abnormal scenario falls outside the existing domain of data sets employed to train the neural network, as judged by the MHS supervisory controller, an off-line training module will be activated to eventually update the neural network. The recommended control strategies will be transmitted to the MHS control for real-time execution. If there is no further abnormal event detected, the dynamic data base (DDB) module simply continues to monitor the MHS activities. The proposed MHS control system combines the features of example based neural network technology and simulation modeling for true intelligent, on-line, pseudo real-time control. Not only will the system assure that feasible material handling control actions be taken, but also it will implement better control decisions through continuous learning from experiences captured as the operation time of the MHS accumulates.
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  • 9
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    Journal of intelligent manufacturing 10 (1999), S. 449-462 
    ISSN: 1572-8145
    Keywords: Control chart ; pattern recognition ; neural network ; simulation
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mechanical Engineering, Materials Science, Production Engineering, Mining and Metallurgy, Traffic Engineering, Precision Mechanics
    Notes: Abstract Abnormal patterns on manufacturing process control charts can reveal potential quality problems due to assignable causes at an early stage, helping to prevent defects and improve quality performance. In recent years, neural networks have been applied to the pattern recognition task for control charts. The emphasis has been on pattern detection and identification rather than more detailed pattern parameter information, such as shift magnitude, trend slope, etc., which is vital for effective assignable cause analysis. Moreover, the identification of concurrent patterns (where two or more patterns exist together) which are commonly encountered in practical manufacturing processes has not been reported. This paper proposes a neural network-based approach to recognize typical abnormal patterns and in addition to accurately identify key parameters of the specific patterns involved. Both single and concurrent patterns can be characterized using this approach. A sequential pattern analysis (SPA) design was adopted to tackle complexity and prevent interference between pattern categories. The performance of the model has been evaluated using a simulation approach, and numerical and graphical results are presented which demonstrate that the approach performs effectively in control chart pattern recognition and accurately identifies the key parameters of the recognized pattern(s) in both single and concurrent pattern circumstances.
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  • 10
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    Journal of intelligent manufacturing 7 (1996), S. 243-250 
    ISSN: 1572-8145
    Keywords: Job-shop scheduling ; real-time dispatching ; simulation ; neural networks
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mechanical Engineering, Materials Science, Production Engineering, Mining and Metallurgy, Traffic Engineering, Precision Mechanics
    Notes: To schedule a job shop, the first task is to select an appropriate scheduling algorithm or rule. Because of the complexity of scheduling problems, no general algorithm sufficient for solving all scheduling problems has yet been developed. Most job-shop scheduling systems offer alternative algorithms for different situations, and experienced human schedulers are needed to select the best dispatching rule in these systems. This paper proposes a new algorithm for job-shop scheduling problems. This algorithm consists of three stages. First, computer simulation techniques are used to evaluate the efficiency of heuristic rules in different scheduling situations. Second, the simulation results are used to train a neural network in order to capture the knowledge which can be used to select the most efficient heuristic rule for each scheduling situation. Finally, the trained neural network is used as a dispatching rule selector in the real-time scheduling process. Research results have shown great potential in using a neural network to replace human schedulers in selecting an appropriate approach for real-time scheduling. This research is part of an ongoing project of developing a real-time planning and scheduling system.
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  • 11
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    Journal of intelligent manufacturing 8 (1997), S. 3-14 
    ISSN: 1572-8145
    Keywords: Production system analysis ; object-oriented approach ; production control ; simulation ; Petri networks
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mechanical Engineering, Materials Science, Production Engineering, Mining and Metallurgy, Traffic Engineering, Precision Mechanics
    Notes: Abstract Tool specification for production system control requires the identification of the main characteristics of the production system. The production systems are varied, and the production control tools (such as scheduling algorithms and resource assignment rules) are often dedicated to only one class of these systems. Tool assessment for production system control requires modelling of the production system. We propose a new approach to production systems, to identify the nature and the complexity of the system according to the classification of Conway et al., and to specify a dynamic model that will allow us to simulate production control decisions. This paper presents this object-oriented approach, which identifies the resources and the organization features of the studied system. It then, proposes some predetermined classes of objects, which enable us to classify the system components and to use pre-existing dynamic models. These dynamic models are based on timed and coloured Petri nets. The overall architecture of our methodology follows three steps: top-down analysis of resources and bottom-up recognition of predetermined objects, instantiation and integration of objects, and implementation of objects. An example illustrates its use in the textile industry.
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  • 12
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    Journal of intelligent manufacturing 8 (1997), S. 405-413 
    ISSN: 1572-8145
    Keywords: Manufacturing systems ; decision making systems ; simulation ; discrete and continuous optimization ; discrete ψ-transform method
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mechanical Engineering, Materials Science, Production Engineering, Mining and Metallurgy, Traffic Engineering, Precision Mechanics
    Notes: Abstract Algorithms for discrete and continuous optimization are a very important part of decision making systems in manufacturing. Most planning, scheduling and layout problems require these algorithms. In practice, research into efficient algorithms meets two principal obstacles. The first one is linked to the fact that quite often the criteria cannot be expressed in an analytic form, so it is not possible to use existing theoretical resolution methods. The second is due to the fact that most of the problems for which the criteria can be represented in analytic form are NP-hard problems. This situation can be simplified using simulation. But the use of simulation and optimization methods together often gives a local optimum. The proposed method in this paper is based on the use of a discrete modification of ψ-transforms jointly with some heuristics for local optimization. The originality of this approach is in the possibility to avoid a local optimum, while using models of simulation for the computation of values of the criteria. An example of the utilization of the method is given: it concerns the optimization of the launching of the parts in production in systems of the job-shop type. The proposed method is compared with a heuristic known to be very good in the same number of simulations. The results of five tests with different model sizes show the efficiency of the proposed method.
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  • 13
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    Journal of intelligent manufacturing 6 (1995), S. 175-190 
    ISSN: 1572-8145
    Keywords: Concurrent engineering ; cell design ; cell control ; simulation ; knowledge-based expert system ; neural networks
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mechanical Engineering, Materials Science, Production Engineering, Mining and Metallurgy, Traffic Engineering, Precision Mechanics
    Notes: Abstract One of the major thrusts of ‘agile/lean/responsive’ manufacturing strategies of the twentyfirst century is to introduce advanced information technology into manufacturing. This paper presents a framework for robust manufacturing system design with the integration of simulation, neural networks and knowledge-based expert system tools. An operation/ cost-driven cell design methodology was applied to concurrently consider cell physical design and the complexity of cell control functions. Simulation was exercised to estimate performance measures based on input parameters and given cell configurations. A rulebased expert system was employed to store the acquired expert knowledge regarding the relation between cell control complexities, cost of cell controls, performance measures and cell configuration. Neural networks were applied to predict the cell design configuration and corresponding complexities of cell control functions. Training of neural networks was performed with both forward and backward methods by using the same pair of data sets. Hence, trained neural networks will be able to predict either input or output parameters. This innovative new design methodology was illustrated via a successful implementation exercise resulting in actually acquiring an automated cell at industrial settings. The experience learned from this exercise indicates that the proposed design methodology works well as an effective decision support system for cell designers and the management in determining appropriate cell configuration and cell control functions at the design stage.
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  • 14
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    Journal of intelligent manufacturing 8 (1997), S. 125-136 
    ISSN: 1572-8145
    Keywords: Artificial intelligence ; simulation ; database management system ; object oriented paradigm ; simulation program generation
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mechanical Engineering, Materials Science, Production Engineering, Mining and Metallurgy, Traffic Engineering, Precision Mechanics
    Notes: Abstract Although many studies have illustrated AI-based simulation, the concept of combining databases with AI and simulation is relatively new. Complementing AI and simulation with databases aids in the development of a completely integrated simulation environment that spans the whole simulation life cycle. This study illustrates the design of a simulation program generator, the intelligent simulation code generator (ISCG), which uses a database management system as the user-oriented interface, an object-oriented system to develop the knowledge base and simulation environment, and a target simulation language as the simulation software. The ISCG offers data independence, system independence, simulation-specific transparency, and target language neutrality. Furthermore, the ISCG offers system design flexibility.
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  • 15
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    Annals of operations research 3 (1985), S. 355-377 
    ISSN: 1572-9338
    Keywords: Flexible manufacturing systems ; scheduling ; manufacturing systems ; simulation ; computer integrated manufacturing
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics , Economics
    Notes: Abstract This paper presents a new two-phase (TP) approximate method for real-time scheduling in a flexible manufacturing system (FMS). This method combines a reduced enumeration schedule generation algorithm with a 0–1 optimization algorithm. In order to make the combined algorithm practicable, heuristic rules are introduced for the selection of jobs to be scheduled. The relative performance of the TP method vis-a-vis conventional heuristic dispatching rules such as SPT, LPT, FCFS, MWKR, and LWKR is investigated using combined process-interaction/discrete-event simulation models. An efficient experimental procedure is designed and implemented using these models, and the statistical analysis of the results is presented. For the particular case investigated, the conclusions are very encouraging. In terms of mean flow time, the TP method performs significantly better than any other tested heuristic dispatching rules. Also, the experimental results show that using global information significantly improves the FMS performance.
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  • 16
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    Annals of operations research 3 (1985), S. 13-21 
    ISSN: 1572-9338
    Keywords: Flexible manufacturing systems ; queueing models ; simulation ; performance evaluation
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics , Economics
    Notes: Abstract Flexible manufacturing systems (FMSs) are a class of automated systems which can be used to improve productivity in discrete parts manufacturing. Due to the complexity of these systems, it is useful to have models that can aid in the design and operation of FMSs. We specifically differentiate here betweengenerative (or prescriptive) models, whichfind candidate decisions, andevaluative (or descriptive) models, whichevaluate a given set of decisions. We briefly cover, in a practical context, the pros and cons of these two classes of models. Then we focus on the latter class of models. Evaluative models for FMSs fall into five main classes, based on the technique used, namely: static allocation, queueing network theory, simulation, perturbation analysis, and Petri nets. Each of these approaches is briefly described, advantages and disadvantages mentioned, and references given to more detailed papers.
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  • 17
    ISSN: 1572-9338
    Keywords: integer programming ; discriminant analysis ; simulation
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics , Economics
    Notes: Abstract Although there have been several journal articles on the classificatory performance of mathematical programming approaches to the two-group discriminant problem, there has been no simulation study on the classificatory performance of mathematical programming approaches to the multiple-group problem reported in the literature. This study reports the results of a simulation experiment on the classificatory performance of a single-function and a multiple-function mathematical programming model relative to that of the standard parametric procedures for the three-group problem with small training samples. The effect of second-order terms on the classificatory performance of the mathematical programming models for the three-group problem is also investigated. Furthermore, this study theoretically examines the range of parameter values of a multiple-function mathematical programming model for which its number of misclassifications in the training sample cannot exceed that of a single-function model.
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  • 18
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    Annals of operations research 74 (1997), S. 321-332 
    ISSN: 1572-9338
    Keywords: simulation ; modeling ; aerospace ; air route structure ; free flight ; clustering
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics , Economics
    Notes: Abstract Recent work performed for the Federal Aviation Administration to support the development of future concepts of air traffic management has involved simulation modeling of patterns of airspace usage by commercial and business air traffic. The objective of these efforts has been to investigate the impacts of a pattern of airspace usage known as "free flight", whereby pilots and flight dispatchers have much more freedom to choose, say, direct or wind-optimal routing through airspace. One of the figures of merit investigated is a count of "convergence pairs" as a measure of the complexity of various traffic patterns. These are cases when aircraft in the simulation model fly close to each other. Interestingly, geographic plots of convergence pairs accumulated over time bring out certain features or patterns of congested air traffic flows or flight alignments. However, these plots are also thick with "noise" or extraneous convergence pairs, whose presence detracts from the ability to perceive congested air traffic flows. Cluster analysis has been found to be an effective method of filtering these displays so that the congested flow features are discernible. The process developed for this purpose is based on a two-pass clustering approach. The process has worked well for the simulation modeling performed to date. Classification of the locations of convergence pairs into congested flow corridors is visually appealing, and has helped distinguish differences in contrasting scenarios of airspace usage. The paper presents graphical results and describes the clustering algorithms employed.
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  • 19
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    International journal of flexible manufacturing systems 7 (1995), S. 339-360 
    ISSN: 1572-9370
    Keywords: Petri net ; FMS ; modeling ; simulation ; tool ; analysis ; animation
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mechanical Engineering, Materials Science, Production Engineering, Mining and Metallurgy, Traffic Engineering, Precision Mechanics
    Notes: Abstract We propose a CAD tool, XPN-FMS, which is primarily based on a unique Petri net (PN) synthesis method, called the knitting technique, developed by the authors. Petri net theory has been applied to specification, validation, performance analysis, control code generation, and simulation for manufacturing systems. The analysis of flexible manufacturing systems (FMSs) based on PNs suffers from the complexity problem of reachability analysis (Peterson, 1981). CAD tools are urgently needed. There is no existing CAD tool for FMSs as comprehensive as XPN-FMS, in the sense that the latter integrates the functions of drawing, analysis, reduction (Chao and Wang, 1992; Murata and Koh, 1980), synthesis, property queries, and animation of FMS operations in one software package. Using the X window graphical interface and animation, XPN-FMS makes the modeling and analysis of an FMS visualizable and easy to understand and manipulate. It lets a user draw the factory layout of an FMS on the screen of a monitor using the supplied tools. A corresponding PN model can also be drawn on the monitor screen. XPN-FMS can animate and simulate the overall operating process of the FMS. It is useful for FMS specification, validation, and exploration of different design alternatives, status monitoring, and control. Using XPN-FMS with various inputs and comparing the resulting outputs, the user can determine how to improve efficiency, reduce cost, and pinpoint bottlenecks. For the PN models of FMSs that are decision free, we extend the theory and algorithm of a unique matrix-based method (Chao and Wang, 1993b) to search for subcritical loops (including types A and B) and to support scheduling and dealing with transition periods. XPN-FMS implements this extended method to find the minimum cycle time, critical loop, subcritical loops, next critical loop, and scheduling ranges to avoid the transient period for static scheduling. This is implemented in XPN-FMS for the input sequence control.
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  • 20
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    International journal of flexible manufacturing systems 8 (1996), S. 23-43 
    ISSN: 1572-9370
    Keywords: FMS ; simulation ; scheduling ; dispatch ; heuristics
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mechanical Engineering, Materials Science, Production Engineering, Mining and Metallurgy, Traffic Engineering, Precision Mechanics
    Notes: Abstract The objective of the research, presented herein, was to determine whether or not the makespan performance of an FMS could be improved by a methodology which draws parallels with the actions of a human chess player in resolving decision problems in an environment where optimal solutions were computationally intractable with current processing technologies. The methodology was given the acronym CHESS (Control Heuristic Embedded System Simulator) and provides a mechanism for using short-term simulation look-aheads to resolve contention problems. The research also sought to determine the relationship between performance improvement and “look-ahead distance.” The results of the research highlight the fact that the methodology could provide considerable reductions in the number of contentions and the makespan time for a given range of part types (approximately 20 percent for the test-case applications). The most pertinent results, however, are those that highlight the effectiveness of look-ahead distance in terms of improving system performance, and these may have a potential to provide a significant impact in a range of different areas.
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  • 21
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    Annals of operations research 8 (1987), S. 363-381 
    ISSN: 1572-9338
    Keywords: Probability ; simulation ; petroleum ; resources ; appraisal
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics , Economics
    Notes: Abstract An analytic probabilistic methodology for resource appraisal of undiscovered oil and gas resources in play analysis is presented. This play-analysis methodology is a geostochastic system for petroleum resource appraisal in explored as well as frontier areas. An objective was to replace an existing Monte Carlo simulation method in order to increase the efficiency of the appraisal process. Underlying the two methods is a single geologic model which considers both the uncertainty of the presence of the assessed hydrocarbon and its amount if present. The results of the model are resource estimates of crude oil, nonassociated gas, dissolved gas, and gas for a geologic play in terms of probability distributions. The analytic method is based upon conditional probability theory and a closed form solution of all means and standard deviations, along with the probabilities of occurrence.
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  • 22
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    Annals of operations research 67 (1996), S. 183-210 
    ISSN: 1572-9338
    Keywords: Capacity planning ; emergency services ; health care ; simulation
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics , Economics
    Notes: Abstract Due to its highly stochastic nature and complex interaction between services involved, health care has been a demanding area of application for computer simulation. This paper includes details and results of a simulation study realized in the Surgical Emergency Department at Istanbul University School of Medicine. The purpose is to suggest new bed capacities to improve the current system, and also to provide the management with guidelines for their expansion plans. For this aim, arrival rates, treatment procedures, inpatient admittance, and service durations have been carefully analyzed and modeled. The model, coded in SLAM-II simulation language, has been run under several bed capacity scenarios, and resulting queueing and waiting patterns have been discussed in detail.
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  • 23
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    Computational & mathematical organization theory 3 (1998), S. 219-247 
    ISSN: 1572-9346
    Keywords: computational models of organizations ; organizational ecology ; cellular automata ; simulation
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Abstract Research on the ecological dynamics oforganizational populations has demonstrated that competitiveconditions at the time of founding have enduring effects onorganizational survival. According to ecological theories,organizational life chances are systematically affected by density (the number of organizations in a population) at thetime of founding because the lower resource endowments thatcharacterize organizations appearing in periods of highpopulation density tend to become self-reinforcing, and—over time—amplify differences in mortality rates oforganizations founded under different conditions. However,credible arguments have been offered that could justify both positive and negative effects of the delayed effectsof population density on organizational mortality rates, andreceived empirical research in part reflects this ambiguity.To develop new insight into this issue and to explore theboundaries of received empirical results, in this study wepresent a computational model of organizational evolutionaccording to which the global dynamics of organizationalpopulations emerge from the iteration of simple rules oflocal interaction among individual organizations. We use the synthetic data produced by simulation to estimate eventhistory models of organizational mortality, and compare theparameter estimates with those reported in the most recentempirical studies of actual organizational populations. Theconclusions supported by the model qualify and extendreceived empirical results, and suggest that delayed effectsof density are highly sensitive the details of local structure of connections among members of organizationalpopulations.
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    Computational & mathematical organization theory 4 (1998), S. 43-69 
    ISSN: 1572-9346
    Keywords: simulation ; organization ; computational model ; formal logic ; cognition
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    Topics: Mathematics
    Notes: Abstract A programming language which is optimized for modelling multi-agent interaction within articulated social structures such as organizations is described with several examples of its functionality. The language is SDML, a strictly declarative modelling language which has object-oriented features and corresponds to a fragment of strongly grounded autoepistemic logic. The virtues of SDML include the ease of building complex models and the facility for representing agents flexibly as models of cognition as well as modularity and code reusability. Two representations of cognitive agents within organizational structures are reported and a Soar-to-SDML compiler is described. One of the agent representations is a declarative implementation of a Soar agent taken from the Radar-Soar model of Ye and Carley (1995). The Ye-Carley results are replicated but the declarative SDML implementation is shown to be much less computationally expensive than the more procedural Soar implementation. As a result, it appears that SDML supports more elaborate representations of agent cognition together with more detailed articulation of organizational structure than we have seen in computational organization theory. Moreover, by representing Soar-cognitive agents declaratively within SDML, that implementation of the Ye-Carley specification is necessarily consistent and sound with respect to the formal logic to which SDML corresponds.
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    Computational & mathematical organization theory 3 (1997), S. 151-171 
    ISSN: 1572-9346
    Keywords: organizational performance ; planned organizational change ; resistance to change ; system dynamics ; simulation
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    Topics: Mathematics
    Notes: Abstract This paper suggests that an induction of change program leads to atemporary impairment of organizational performance. A System Dynamics Modelportrays the process of planned organizational change. A set of keyvariables that facilitate or impede change is identified, quantified, andintegrated into the model. Three data sets, reproduced by simulation,demonstrate that the model is internally consistent and empiricallyadequate. The paper discusses theoretical and practical implications of the‘initial dip’ phenomenon in processes of planned change.
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    International journal of flexible manufacturing systems 11 (1999), S. 271-289 
    ISSN: 1572-9370
    Keywords: random flexible manufacturing systems ; scheduling ; simulation
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    Topics: Mechanical Engineering, Materials Science, Production Engineering, Mining and Metallurgy, Traffic Engineering, Precision Mechanics
    Notes: Abstract The increased use of flexible manufacturing systems to efficiently provide customers with diversified products has created a significant set of operational challenges for managers. Many issues concerning procedures and policies for the day-to-day operation of these systems still are unresolved. Previous studies in this area have concentrated on various problems by isolating or simplifying the systems under study. The primary objective of this study is to extend previous research by examining the effects of scheduling rules and routing flexibility on the performance of a constrained, random flexible manufacturing system (FMS). Other experimental factors considered are shop load, shop configuration, and system breakdowns. Within the bounds of this experiment, the results indicate that, in the presence of total routing flexibility, the effects of shop load, system breakdowns, and scheduling rules are significantly dampened. In particular, when total routing flexibility exists, the choice of scheduling rules is not critical. We also show that the behavior of scheduling rules in a more constrained FMS environment (i.e., where system breakdowns occur and material handling capability is limited) is consistent with the findings of previous research conducted under less constrained environments. Finally, results indicate that the shop configuration factor has little or no impact on a system's flow-time performance.
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    International journal of flexible manufacturing systems 7 (1995), S. 27-46 
    ISSN: 1572-9370
    Keywords: automatic assembly systems ; genetic algorithms ; simulation ; stochastic optimization
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    Topics: Mechanical Engineering, Materials Science, Production Engineering, Mining and Metallurgy, Traffic Engineering, Precision Mechanics
    Notes: Abstract This paper presents the application of genetic algorithms to the performance optimization of asynchronous automatic assembly systems (AAS). These stochastic systems are subject to blocking and starvation effects that make complete analytic performance modeling difficult. Therefore, this paper extends genetic algorithms to stochastic systems. The performance of the genetic algorithm is measured through comparison with the results of stochastic quasi-gradient (SQM) methods to the same AAS. The genetic algorithm performs reasonably well in obtaining good solutions (as compared with results of SQM) in this stochastic optimization example, even though genetic algorithms were designed for application to deterministic systems. However, the genetic algorithm's performance does not appear to be superior to SQM.
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    International journal of flexible manufacturing systems 7 (1995), S. 255-286 
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    Keywords: productivity ; design process ; robotic assembly ; simulation
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    Topics: Mechanical Engineering, Materials Science, Production Engineering, Mining and Metallurgy, Traffic Engineering, Precision Mechanics
    Notes: Abstract The design of production systems is generally based on economic considerations, which are related to certain technical criteria, such as capacity, availability, and reliability. To realize a cost-effective design, these technical and economic criteria should be considered in their mutual coherence during the conceptual design process. This paper focuses on a productivity model, which is related to this subject. This model allows an opinion to be formed about the technical and economic performance of conceptual robotic assembly cells, during the process of design. First, the system design process is discussed in brief, after which the productivity variables are presented. An illustration of the model is used to assess the technical and economic behavior of alternative system structures for the assembly of a power plug assortment.
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    Computational & mathematical organization theory 5 (1999), S. 167-192 
    ISSN: 1572-9346
    Keywords: rational choice ; friendship ; Markov processes ; random utility models ; simulation ; empirical test
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    Topics: Mathematics
    Notes: Abstract We propose a class of actor-oriented statistical models for closed social networks in general, and friendship networks in particular. The models are random utility models developed within a rational choice framework. Based on social psychological and sociological theories about friendship, mathematical functions capturing expected utility of individual actors with respect to friendship are constructed. Expected utility also contains a random (unexplained) component. We assume that, given their restrictions and contact opportunities, individuals evaluate their utility functions and behave such that they maximize the expected amount of utility. The behavior under consideration is the expression of like and dislike (choice of friends). Theoretical mechanisms that are modelled are, e.g., the principle of diminishing returns, the tendency towards reciprocated choices, and the preference for friendship relations with similar others. Constraints imposed on individuals are, e.g., the structure of the existing network, and the distribution of personal characteristics over the respondents. The models are illustrated by means of a data-set collected among university freshmen at 7 points in time during 1994 and 1995.
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    International journal of flexible manufacturing systems 11 (1999), S. 19-35 
    ISSN: 1572-9370
    Keywords: integration ; process planning ; simulation
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    Topics: Mechanical Engineering, Materials Science, Production Engineering, Mining and Metallurgy, Traffic Engineering, Precision Mechanics
    Notes: Abstract Many studies on integration of process planning and production scheduling have been carried out during the last decade. While various integration approaches and algorithms have been proposed, the implementation of these approaches is still a difficult issue. To achieve successful implementation, it is important to examine and evaluate integration approaches or algorithms beforehand. Based on an object-oriented integration testbed, a simulation study that compares different integration algorithms is presented in this paper. Separated planning method and integrated planning methods are examined. Also, situations of both fixed and variable processing times are simulated, and useful results have been observed. The successful simulation with the object-oriented integration testbed eventually will be extended to include other new planning algorithms for examining their effectiveness and implementation feasibility.
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    Annals of operations research 15 (1988), S. 269-287 
    ISSN: 1572-9338
    Keywords: Production scheduling ; integer programming ; simulation ; flexible manufacturing ; hierarchical modelling
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    Topics: Mathematics , Economics
    Notes: Abstract This study reports the development of a production scheduling system for the integrated management of production in large-scale, high-volume electronic assembly lines. The development of the system incorporates control and planning considerations by addressing the interaction of various subsystems. Stochastic and deterministic aspects of the problem environment are appropriately handled via relevant simulation and analytic models. By effecting a hierarchical breakdown of the problem environment, the system produces information used in practical decision making for production planning and scheduling. Procedures used encompass and address considerations for management of work-in-process, optimization of the various subsystems' performance, minimization of setup time effect, and inventory carrying costs.
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    Annals of operations research 3 (1985), S. 379-391 
    ISSN: 1572-9338
    Keywords: Flexible manufacturing systems ; discrete event systems ; real-time systems ; monitoring ; simulation ; performance evaluation ; perturbation analysis
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    Topics: Mathematics , Economics
    Notes: Abstract The recent perturbation analysis approach to discrete event systems is applied to flexible manufacturing systems (FMS). While analytic (queueing) models are useful in preliminary design of such systems, they are not accurate enough at the detailed design/operation stage. Thus, experimentation on detailed simulations or on the actual system has been the way to optimize system performance. Perturbation analysis allows us to derive the sensitivity of system performance, with respect to several design/operating parameters, by observing a single experiment (and without having to actually alter the parameters — often a costly operation). Thus, observation of one experiment can give accurate directions for the improvement of several parameter values. Here we give a simulation example illustrating how perturbation analysis could be used on-line on an FMS to improve its performance, including reducing its operating cost. Experimental results are also presented validating the estimates obtained from this technique.
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    Annals of operations research 74 (1997), S. 239-257 
    ISSN: 1572-9338
    Keywords: autocorrelation ; L 1 regression ; least absolute deviations ; robust regression ; simulation
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    Topics: Mathematics , Economics
    Notes: Abstract Least absolute value (LAV) regression provides a robust alternative to least squares, particularly when the disturbances follow distributions that are nonnormal and subject to outliers. While inference in least squares estimation is well-understood, inferential procedures in the context of LAV estimation have not been studied as extensively, particularly in the presence of non-independent disturbances. In this work, we study three alternative significance test procedures in LAV regression, along with two approaches used to correct for serial correlation. The study is based on large-scale Monte Carlo simulations, and comparisons are made based on both observed significance levels and power.
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    International journal of flexible manufacturing systems 9 (1997), S. 273-298 
    ISSN: 1572-9370
    Keywords: routing flexibility ; dynamic sequencing and dispatching ; simulation ; Taguchi experimental design
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    Topics: Mechanical Engineering, Materials Science, Production Engineering, Mining and Metallurgy, Traffic Engineering, Precision Mechanics
    Notes: Abstract The evolving manufacturing environment is characterized by a drive toward increasing flexibility. One possible manifestation of flexibility within an FMS is in the form of routing flexibility. Providing this typically is an expensive proposition, and system designers therefore aim to provide only the required levels commensurate with a given set of operating conditions. This paper presents a framework based on a Taguchi experimental design for studying the nature of the impact of varying levels of routing flexibility on the performance of an FMS. Simulation results indicate that increases in routing flexibility, when made available at the cost of an associated penalty on operation processing time, is not always beneficial. There is an optimal flexibility level, beyond which system performance deteriorates, as judged by the makespan measure of performance. It is suggested that the proposed methodology can be used in practice for not only setting priorities on specific design and control factors but also for highlighting likely factor level combinations that could yield near-optimal shop performance.
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    International journal of flexible manufacturing systems 9 (1997), S. 167-193 
    ISSN: 1572-9370
    Keywords: flexible manufacturing systems ; decentralization ; stochastic equilibrium ; pricing ; benefits ; simulation
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    Topics: Mechanical Engineering, Materials Science, Production Engineering, Mining and Metallurgy, Traffic Engineering, Precision Mechanics
    Notes: Abstract Flexible manufacturing systems (FMSs) can apply the efficiencies of large-scale production to small batch production. The coordination of FMS activities is a complex task; this paper presents a decentralized pricing mechanism that can be used to estimate the activity–based costs and manage the activities of the FMS efficiently. The pricing mechanism described in this paper does not require systemwide information to compute prices; instead, the pricing mechanism samples and uses the demand information at each CNC machine to compute rental prices at that machine. We derive the theoretical formula for rental prices supporting the optimal performance and propose simulation studies to estimate the rental prices for real-time price changes in a decentralized manner. Results from a preliminary simulation study indicate that stable rental prices can be estimated and significant improvements can be realized by using the pricing mechanism.
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    Journal of computational analysis and applications 1 (1999), S. 349-385 
    ISSN: 1572-9206
    Keywords: Estimation ; geometric compound ; heavy-tail modeling ; Linnik distribution ; Mittag–Leffler law ; mixture ; multivariate Laplace distribution ; random summation ; simulation ; subordination
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    Topics: Mathematics
    Notes: Abstract The paper discusses recent advances in the theory of multivariate geometric stable (GS) distributions. The results presented include characterizations, mixture representations, properties, simulation, and estimation.
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    Annals of operations research 15 (1988), S. 227-267 
    ISSN: 1572-9338
    Keywords: FMS ; production ratios ; mathematical programming ; levels of detail in modeling ; balanced machine workloads ; machine utilizations ; dispatching rules ; simulation
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    Topics: Mathematics , Economics
    Notes: Abstract Stecke [21] has developed mathematical programming approaches for determining, from a set of part type requirements, the production ratios (part types to be produced next, and their proportions) which maximize overall machine utilizations by balancing machine workloads in a flexible manufacturing system (FMS). These mathematical programming (MP) approaches are aggregate in the sense that they do not take into account such things as contention for transportation resources, travel time for work-in-process, contention for machines, finite buffer space, and dispatching rules. In the current study, the sensitivity of machine utilizations to these aggregations is investigated through simulation modeling. For the situation examined, it is found that achieved machine utilizations are a strong function of some of the factors ignored in the MP methodology, ranging from 9.1% to 22.9% less than those theoretically attainable under the mathematical programming assumptions. The 9.1% degradation results from modeling with nonzero work-in-process travel times (i.e. 2 minutes per transfer) and using only central work-in-process buffers. Resource levels (e.g. the number of automated guided vehicles; the amount of work-in-process; the number of slack buffers) needed to limit the degradation to 9.1% correspond to FMS operating conditions which are feasible in practice.
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    Annals of operations research 73 (1997), S. 233-252 
    ISSN: 1572-9338
    Keywords: Data Envelopment Analysis ; model specification ; simulation
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    Topics: Mathematics , Economics
    Notes: Abstract The use of Data Envelopment Analysis for estimating comparative efficiency has become widespread, and there has been considerable academic attention paid to the development of variants of the basic DEA model. However, one of the principal weaknesses of DEA is that - unlike statistically based methods - it yields no diagnostics to help the user determine whether or not the chosen model is appropriate. In particular, the choice of inputs and out-puts depends solely on the judgement of the user. The purpose of this paper is to examine the implications for efficiency scores of using a misspecified model. A simple production process is set up. Simulation models are then used to explore the effects of applying misspecified DEA models to this process. The phenomena investigated are: the omission of significant variables; the inclusion of irrelevant variables; and the adoption of an inappropriate variable returns to scale assumption. The robustness of the results is investigated in relation to sample size; variations in the number of inputs; correlation between inputs; and variations in the importance of inputs. The paper concludes that the dangers of misspecification are most serious when simple models are used and sample sizes are small. In such circumstances, it is concluded that it will usually be to the modeller's advantage to err on the side of including possibly irrelevant variables rather than run the risk of excluding a potentially important variable from the model.
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    Computational & mathematical organization theory 2 (1996), S. 171-195 
    ISSN: 1572-9346
    Keywords: organization design ; simulation ; organization modeling ; organizational analysis tools
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    Topics: Mathematics
    Notes: Abstract Large scale and multidisciplinary engineering projects (e.g., design of a hospital building) are often complex. They usually involve many interdependent activities and require intensive coordination among actors (i.e., designers) to deal with activity interdependencies. To make such projects more effective and efficient, one needs to understand how coordination requirements are generated and what coordination mechanisms should be applied for given project situations. Our research on the Virtual Design Team (VDT) attempts to develop a computational model of project organizations to analyze how activity interdependencies raise coordination needs and how organization design and communication tools change team coordination capacity and project performance. The VDT model is built based on contingency theory (Galbraith, 1977) and our observations about collaborative and multidisciplinary work in large, complex projects. VDT explicitly models actors, activities, communication tools and organizations. Based on our extended information-processing view of organizations, VDT simulates the actions of, and interactions among actors as processes of attention allocation, capacity allocation, and communication. VDT evaluates organization performance by measuring emergent project duration, direct cost, and coordination quality. The VDT model has been tested internally, and evaluated externally through case-studies. We found three way qualitative consistency among predictions of the simulation model, of organization theory, and of experienced project managers. In this paper, we present the VDT model in detail and discuss some general issues involved in computational organization modeling, including level of abstraction of tasks and actors' reasoning, and model validation.
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    Annals of operations research 8 (1987), S. 243-256 
    ISSN: 1572-9338
    Keywords: Control variates ; Monte Carlo ; nonlinear estimation ; simulation ; variance reduction
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    Topics: Mathematics , Economics
    Notes: Abstract The sampling distribution of parameter estimators can be summarized by moments, fractiles or quantiles. For nonlinear models, these quantities are often approximated by power series, approximated by transformed systems, or estimated by Monte Carlo sampling. A control variate approach based on a linear approximation of the nonlinear model is introduced here to reduce the Monte Carlo sampling necessary to achieve a given accuracy. The particular linear approximation chosen has several advantages: its moments and other properties are known, it is easy to implement, and there is a correspondence to asymptotic results that permits assessment of control variate effectiveness prior to sampling via measures of nonlinearity. Empirical results for several nonlinear problems are presented.
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    Annals of operations research 8 (1987), S. 351-362 
    ISSN: 1572-9338
    Keywords: Response surface methodology ; simulation ; optimization
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    Topics: Mathematics , Economics
    Notes: Abstract Managing the volume of experimental and/or simulation data required for large-scale design studies can be a significant problem. This paper describes a method for dealing with this problem, using response surface methodology. The method involves (1) determining a summary parameterization of the response of the underlying process mechanism generating the data, in order to characterize this response in terms of a manageable set of performance measures, and (2) deriving a model of the data, in order to summarize the dependence of the performance measures on selected predictor or design variables. The method is illustrated by its application to a problem in vehicle collision research.
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    Computational & mathematical organization theory 4 (1998), S. 71-95 
    ISSN: 1572-9346
    Keywords: organization modeling ; health care ; simulation ; medical protocols ; representation
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    Topics: Mathematics
    Notes: Abstract Organizational simulations have been used in business, manufacturing, and engineering design tasks to gain insight into organizational process bottlenecks, and to improve the quality and efficiency of processes within these industries. As market pressures demand increased efficiencies within the health care industry, organizational simulation techniques could provide similar insight into the design of better medical care processes, or protocols, in medical organizations. To simulate the process of medical care within a specific organization however, requires models that can represent (1) unpredictable patient responses to care, (2) the flexibility needed to adapt to different patients, and (3) different preferences of health care professionals and the implicit preferences contained within the protocol. Using previous work on simulation in the Virtual Design Team (VDT), and an example protocol drawn from an existing protocol in bone marrow transplantation, we describe extensions to the VDT information-processing representation that will allow us to simulate the performance characteristics of a medical protocol used within a medical organization. Our representational extensions capture the uncertainty of medical care for patients, the activity flexibility within the organization, and the preferences of health care professionals that will make information-processing organizational simulations in the medical domain possible. We believe our representation will provide a robust simulation “tool box” that can be used to investigate the performance of specific medical protocols within different hospital settings, and explore organizational theory within the health care industry.
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    Advances in computational mathematics 9 (1998), S. 337-352 
    ISSN: 1572-9044
    Keywords: fast Fourier transform ; nonequispaced grids ; B-splines ; Gaussian bells ; shift-invariant spaces ; 65T10 ; 41A15 ; 41A30 ; 42A16
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    Topics: Mathematics
    Notes: Abstract In this paper, we are concerned with fast Fourier transforms for nonequispaced grids. We propose a general efficient method for the fast evaluation of trigonometric polynomials at nonequispaced nodes based on the approximation of the polynomials by special linear combinations of translates of suitable functions ϕ. We derive estimates for the approximation error. In particular, we improve the estimates given by Dutt and Rokhlin [7]. As a practical consequence, we obtain a criterion for the choice of the parameters involved in the fast transforms.
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    Advances in computational mathematics 11 (1999), S. 1-10 
    ISSN: 1572-9044
    Keywords: median ; interpolation ; polynomial ; spline ; 41A05 ; 41A10 ; 41A15
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    Topics: Mathematics
    Notes: Abstract We study the median of a continuous function on an interval and show that for certain spaces of functions there is a unique function in the space whose medians on given intervals take given values.
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    ISSN: 1572-9125
    Keywords: 65F10 ; Semiconductors ; simulation ; partial differential equations
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    Notes: Abstract The alternate-block-factorization (ABF) method is a procedure for partially decoupling systems of elliptic partial differential equations by means of a carefully chosen change of variables. By decoupling we mean that the ABF strategy attempts to reduce intra-equation coupling in the system rather than intra-grid coupling for a single elliptic equation in the system. This has the effect of speeding convergence of commonly used iteration schemes, which use the solution of a sequence of linear elliptic PDEs as their main computational step. Algebraically, the change of variables is equivalent to a postconditioning of the original system. The results of using ABF postconditioning on some problems arising from semiconductor device simulation are discussed.
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    Advances in computational mathematics 9 (1998), S. 145-171 
    ISSN: 1572-9044
    Keywords: periodic pseudodifferential equations ; multiwavelets ; splines with multiple knots ; generalized Galerkin–Petrov schemes ; boundary element methods ; error analysis ; stability ; Strang–Fix condition ; 65J10 ; 65N30 ; 65N35 ; 65R20 ; 47G30 ; 45P05 ; 41A25 ; 41A30 ; 41A15
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    Notes: Abstract We develop a stability and convergence analysis of Galerkin–Petrov schemes based on a general setting of multiresolution generated by several refinable functions for the numerical solution of pseudodifferential equations on smooth closed curves. Particular realizations of such a multiresolution analysis are trial spaces generated by biorthogonal wavelets or by splines with multiple knots. The main result presents necessary and sufficient conditions for the stability of the numerical method in terms of the principal symbol of the pseudodifferential operator and the Fourier transforms of the generating multiscaling functions as well as of the test functionals. Moreover, optimal convergence rates for the approximate solutions in a range of Sobolev spaces are established.
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    Advances in computational mathematics 9 (1998), S. 251-279 
    ISSN: 1572-9044
    Keywords: bivariate splines ; approximation order by splines ; stable approximation schemes ; super-splines ; 41A15 ; 41A63 ; 41A25 ; 65D10
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    Topics: Mathematics
    Notes: Abstract We show how to construct stable quasi-interpolation schemes in the bivariate spline spaces S d r (Δ) with d⩾ 3r + 2 which achieve optimal approximation order. In addition to treating the usual max norm, we also give results in the L p norms, and show that the methods also approximate derivatives to optimal order. We pay special attention to the approximation constants, and show that they depend only on the smallest angle in the underlying triangulation and the nature of the boundary of the domain.
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    Advances in computational mathematics 11 (1999), S. 81-104 
    ISSN: 1572-9044
    Keywords: refinable functions ; interpolatory subdivision scheme wavelets ; 41A15 ; 42A05 ; 42A15 ; 41A30
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    Topics: Mathematics
    Notes: Abstract This paper provides several constructions of compactly supported wavelets generated by interpolatory refinable functions. It was shown in [7] that there is no real compactly supported orthonormal symmetric dyadic refinable function, except the trivial case; and also shown in [10,18] that there is no compactly supported interpolatory orthonormal dyadic refinable function. Hence, for the dyadic dilation case, compactly supported wavelets generated by interpolatory refinable functions have to be biorthogonal wavelets. The key step to construct the biorthogonal wavelets is to construct a compactly supported dual function for a given interpolatory refinable function. We provide two explicit iterative constructions of such dual functions with desired regularity. When the dilation factors are larger than 3, we provide several examples of compactly supported interpolatory orthonormal symmetric refinable functions from a general method. This leads to several examples of orthogonal symmetric (anti‐symmetric) wavelets generated by interpolatory refinable functions.
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    Advances in computational mathematics 11 (1999), S. 287-314 
    ISSN: 1572-9044
    Keywords: Hilbert space ; interpolating splines ; minimization ; thin plate splines ; multiquadric splines ; radial basis functions ; 65D05-65D07-65D10 ; 41A15
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    Topics: Mathematics
    Notes: Abstract The multivariate interpolating (m, l, s)-splines are a natural generalization of Duchon's thin plate splines (TPS). More precisely, we consider the problem of interpolation with respect to some finite number of linear continuous functionals defined on a semi-Hilbert space and minimizing its semi-norm. The (m, l, s)-splines are explicitly given as a linear combination of translates of radial basis functions. We prove the existence and uniqueness of the interpolating (m, l, s)-splines and investigate some of their properties. Finally, we present some practical examples of (m, l, s)-splines for Lagrange and Hermite interpolation.
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    Advances in computational mathematics 4 (1995), S. 389-396 
    ISSN: 1572-9044
    Keywords: B-splines ; positive definite functions ; multivariate interpolation ; 41A05 ; 41A15 ; 41A30 ; 41A63 ; 65D07 ; 65D10
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    Notes: Abstract We construct a new class of positive definite and compactly supported radial functions which consist of a univariate polynomial within their support. For given smoothness and space dimension it is proved that they are of minimal degree and unique up to a constant factor. Finally, we establish connections between already known functions of this kind.
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    BIT 26 (1986), S. 527-536 
    ISSN: 1572-9125
    Keywords: 41A15
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    Notes: Abstract For given data (x i, fi) i=0 n (x 0〈x 1〈...〈x n) we consider the possibility of finding a spline functions of arbitrary degreek (k≧3) with preassigned smoothnessl, where 1≦l≦[(k-1)/2]. The splines should be such thats(x i)=f i (i=0, 1,...,n) ands is convex or nondecreasing and convex on [x 0,x n]. An explicit formula for this function as well as the conditions that guarantee the required properties are established. An algorithm for the determination of the splines and the error bounds is also included.
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    BIT 27 (1987), S. 282-284 
    ISSN: 1572-9125
    Keywords: 65D07 ; 41A15
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    BIT 28 (1988), S. 329-339 
    ISSN: 1572-9125
    Keywords: 65D07 ; 41A15
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    Topics: Mathematics
    Notes: Abstract For a given histogram, we consider an application of a simple rational spline to a shape preserving area true approximation of the histogram. An algorithm for determination of the spline is as easy as one with a quadratic polynomial spline, while the latter does not always preserve the shape of the histogram. Some numerical examples are given at the end of the paper.
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    BIT 28 (1988), S. 340-352 
    ISSN: 1572-9125
    Keywords: 65D17 ; 41A15 ; 90C20 ; Positivity of cubic polynomials ; nonnegative spline interpolants minimal curvature ; dual program ; return-formula
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    Topics: Mathematics
    Notes: Abstract A criterion for the positivity of a cubic polynomial on a given interval is derived. By means of this result a necessary and sufficient condition is given under which cubicC 1-spline interpolants are nonnegative. Further, since such interpolants are not uniquely determined, for selecting one of them the geometric curvature is minimized. The arising optimization problem is solved numerically via dualization.
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    BIT 28 (1988), S. 671-677 
    ISSN: 1572-9125
    Keywords: I.6.1 ; I.6.3 ; simulation ; Bernoulli ; binomial ; uniform sums ; 0–1 arrays
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    Topics: Mathematics
    Notes: Abstract Sums of independent, identically distributed (iid) binomial variates have binomial distributions; yet it is possible to construct a sequence of binomial distributions over {0, 1} for variatesX 1,X 2, ... such that all partial sumsY i =X 1 + ... +X i have uniform distributions. The price to pay is to give up the iid condition. Requiring the property of only one sum does not alleviate the situation much. It is also possible to generate on a computerm × n-matrices, of 0–1 binomial variates with uniformly distributed row and column sums of all major submatrices, but only for smallm andn. Even a three-dimensional 2 × 2 × 2 array can have a similar property. Other target distributions than the rectangular are possible, but cumbersome. An example with smaller variance is given. The results were needed for simulating the performance of some Operations Research algorithms.
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    BIT 29 (1989), S. 140-147 
    ISSN: 1572-9125
    Keywords: AMS(MOS) 65D07 ; 41A15
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    Topics: Mathematics
    Notes: Abstract A method is presented for the construction of positive rational splines of continuity classC 2.
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    BIT 29 (1989), S. 155-156 
    ISSN: 1572-9125
    Keywords: 41A15 ; 65D07 ; B-splines ; Gaffney's identity ; recurrence relations
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    BIT 7 (1967), S. 91-95 
    ISSN: 1572-9125
    Keywords: Relay ; network ; simulation ; program
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    Topics: Mathematics
    Notes: Abstract The program described here has been tried out in order to simulate a relay network with such a degree of complexity, that its function can not be satisfactorly surveyed with manual methods. Since the program has a separate part, which translates Boolean equations and conditions of time delay written symbolically into the machine language, the program has got greater range of application and can be used for simulation of all systems, which can be represented in that way.
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    Advances in computational mathematics 7 (1997), S. 455-545 
    ISSN: 1572-9044
    Keywords: subdivision ; refinable functions ; regularity ; multiwavelets ; 39B12 ; 41A15 ; 41A25 ; 65D99
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    Topics: Mathematics
    Notes: Abstract The motivation for this paper is an interesting observation made by Plonka concerning the factorization of the matrix symbol associated with the refinement equation for B-splines with equally spaced multiple knots at integers and subsequent developments which relate this factorization to regularity of refinable vector fields over the real line. Our intention is to contribute to this train of ideas which is partially driven by the importance of refinable vector fields in the construction of multiwavelets. The use of subdivision methods will allow us to consider the problem almost entirely in the spatial domain and leads to exact characterizations of differentiability and Hölder regularity in arbitrary L p spaces. We first study the close relationship between vector subdivision schemes and a generalized notion of scalar subdivision schemes based on bi-infinite matrices with certain periodicity properties. For the latter type of subdivision scheme we will derive criteria for convergence and Hölder regularity of the limit function, which mainly depend on the spectral radius of a bi-infinite matrix induced by the subdivision operator, and we will show that differentiability of the limit functions can be characterized by factorization properties of the subdivision operator. By switching back to vector subdivision we will transfer these results to refinable vectors fields and obtain characterizations of regularity by factorization and spectral radius properties of the symbol associated to the refinable vector field. Finally, we point out how multiwavelets can be generated from orthonormal refinable bi-infinite vector fields.
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    Advances in computational mathematics 8 (1998), S. 221-247 
    ISSN: 1572-9044
    Keywords: orthonormal scaling function ; smoothness ; symmetry ; wavelets ; 42C05 ; 41A15 ; 42C15 ; 43A30 ; 41A30 ; 39B62
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    Notes: Abstract It is well known that in the univariate case, up to an integer shift and possible sign change, there is no dyadic compactly supported symmetric orthonormal scaling function except for the Haar function. In this paper we are concerned with the construction of symmetric orthonormal scaling functions with dilation factor d=4. Several examples of such orthonormal scaling functions are provided in this paper. In particular, two examples of C 1 orthonormal scaling functions, which are symmetric about 0 and 1/6, respectively, are presented. We will then discuss how to construct symmetric wavelets from these scaling functions. We explicitly construct the corresponding orthonormal symmetric wavelets for all the examples given in this paper.
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    Advances in computational mathematics 8 (1998), S. 353-366 
    ISSN: 1572-9044
    Keywords: triangular finite elements ; Hermite interpolation ; Lagrange interpolation ; 65D05 ; 65D07 ; 65N30 ; 41A05 ; 41A15
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    Notes: Abstract Let Δ(1) be the uniform three direction mesh of the plane whose vertices are integer points of $$\mathbb{Z}^2 $$ .Let $$\Delta _C^{(1)} $$ (respectively $$\Delta _P^{(1)} $$ $$C^r (\mathbb{R}^2 )$$ of degree d=3r (respectively d=3r+1 ) for r odd (respectively even) on the triangulation $$\Delta _C^{(1)} $$ , and of degree d=2r (respectively d=2r+1) for r odd (respectively even) on the triangulation $$\Delta _P^{(1)} $$ . Using linear combinations of translates of these splines we obtain Lagrange interpolants whose corresponding order of approximation is optimal.
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    Advances in computational mathematics 9 (1998), S. 353-362 
    ISSN: 1572-9044
    Keywords: monotonicity ; shape preservation ; tensor-product surfaces ; Bernstein polynomials ; B-splines ; trigonometric polynomials ; control net ; 65D17 ; 41A15
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    Notes: Abstract This paper studies systems of tensor-product functions for which the functions they span are monotonic in any direction when their control nets are monotonic in that direction. It is shown that Bernstein polynomials and B-splines have this property but that totally positive systems in general, such as certain trigonometric and rational bases, do not.
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    Advances in computational mathematics 6 (1996), S. 25-45 
    ISSN: 1572-9044
    Keywords: Bivariate approximation ; segment approximation ; bivariate splines ; functionals ; 41A15 ; 41A63 ; 65D07
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    Notes: Abstract The problem to determine partitions of a given rectangle which are optimal for segment approximation (e.g., by bivariate piecewise polynomials) is investigated. We give criteria for optimal partitions and develop algorithms for computing optimal partitions of certain types. It is shown that there is a surprising relationship between various types of optimal partitions. In this way, we obtain good partitions for interpolation by tensor product spline spaces. Our numerical examples show that the methods work efficiently.
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    Advances in computational mathematics 6 (1996), S. 191-206 
    ISSN: 1572-9044
    Keywords: Triangular finite elements ; bivariate Hermite interpolation ; 41A15 ; 41A05 ; 65D07 ; 65D05 ; 65N30
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    Notes: Abstract Letτ be the triangulation generated by a uniform three direction mesh of the plane. Letτ 6 be the Powell-Sabin subtriangulation obtained by subdividing each triangleT ∈τ by connecting each vertex to the midpoint of the opposite side. Given a smooth functionu, we construct a piecewise polynomial functionυ ∈C r (ℝ2) of degreen=2r (resp. 2r+1) forr odd (resp. even) in each triangle ofτ 6, interpolating derivatives ofu up to orderr at the vertices ofτ.
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    Advances in computational mathematics 8 (1998), S. 19-31 
    ISSN: 1572-9044
    Keywords: cubatures ; spline approximation ; finite‐part integrals ; 65D32 ; 41A15
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    Notes: Abstract In this paper cubature formulas based on bivariate C 1 local polynomial splines with a four directional mesh [4] are generated and studied. Some numerical results with comparison with other methods are given. Moreover the method proposed is applied to the numerical evaluation of 2‐D singular integrals defined in the Hadamard finite part sense. Computational features, convergence properties and error bounds are proved.
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    Advances in computational mathematics 5 (1996), S. 31-49 
    ISSN: 1572-9044
    Keywords: Wavelet transform ; inf-convolution splines ; edge detection ; signal processing ; 41A05 ; 41A15 ; 65D05 ; 65D07
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    Notes: Abstract We present a method for signal reconstruction based upon the location of its singularities which are identified by a wavelet transform technique. The reconstructed signal is an infconvolution spline approximant. The data for the interpolation problem which we solve comes from a compact signal coding procedure. Error bounds and convergence results for the calculated signal are given.
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    Advances in computational mathematics 5 (1996), S. 95-123 
    ISSN: 1572-9044
    Keywords: Analytic wavelet ; non-stationary wavelet ; radial function ; shift-invariant space ; time-frequency window ; Littlewood-Paley identity ; 41A15 ; 41A30 ; 42C15 ; 65D15
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    Notes: Abstract In this paper, we deal with a class of non-stationary multiresolution analysis and wavelets generated by certain radial basis functions. These radial basis functions are noted for their effectiveness in terms of “projection”, such as interpolation and least-squares approximation, particularly when the data structure is scattered or the dimension of ℝ s is large. Thus projecting a functionf onto a suitable multiresolution space is relatively easy here. The associated multiresolution spaces approximate sufficiently smooth functions exponentially fast. The non-stationary wavelets satisfy the Littlewood-Paley identity so that perfect reconstruction of wavelet decompositions is achieved. For the univariate case, we give a detailed analysis of the time-frequency localization of these wavelets. Two numerical examples for the detection of singularities with analytic wavelets are provided.
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    Acta applicandae mathematicae 7 (1986), S. 1-34 
    ISSN: 1572-9036
    Keywords: 41A15 ; 65N30 ; Parabolic systems ; parameter estimation ; approximation methods
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    Topics: Mathematics
    Notes: Abstract A spatially and temporally discrete numerical approximation scheme is developed for the identification of a class of semilinear parabolic systems with unknown boundary parameters. The identification problem is formulated as a least squares fit to data subject to an equivalent representation for the dynamics in the form of an abstract evolution equation. Finite-dimensional difference equation state approximations are constructed using a cubic spline-based, Galerkin method and the Padé rational function approximations to the exponential. A sequence of approximating identification problems result, the solutions of which are shown to exist and, in a certain sense, approximate solutions to the original identification problem. Numerical results for two examples, one involving the modeling of biological mixing in deep sea sediment cores, and the other, the estimation of transport parameters for indoor mixing, are discussed. In both examples, the identification is based upon actual experimental data.
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    Extremes 1 (1998), S. 111-126 
    ISSN: 1572-915X
    Keywords: Poisson process ; scan statistic ; approximation ; simulation
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    Topics: Mathematics
    Notes: Abstract Given a Poisson process in two or three dimensions, we are interested in the scan statistic, i.e. the largest number of points contained in a translate of a fixed scanning set restricted to lie inside a rectangular area. The distribution of the scan statistic is accurately approximated for rectangular scanning sets, using a technique that is also extended to higher dimensions. The accuracy of the approximation is checked through simulation.
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    Methodology and computing in applied probability 1 (1999), S. 127-190 
    ISSN: 1387-5841
    Keywords: combinatorial optimization ; global optimization ; importance sampling ; markov chain monte carlo ; simulated annealing ; simulation
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    Topics: Mathematics
    Notes: Abstract We present a new and fast method, called the cross-entropy method, for finding the optimal solution of combinatorial and continuous nonconvex optimization problems with convex bounded domains. To find the optimal solution we solve a sequence of simple auxiliary smooth optimization problems based on Kullback-Leibler cross-entropy, importance sampling, Markov chain and Boltzmann distribution. We use importance sampling as an important ingredient for adaptive adjustment of the temperature in the Boltzmann distribution and use Kullback-Leibler cross-entropy to find the optimal solution. In fact, we use the mode of a unimodal importance sampling distribution, like the mode of beta distribution, as an estimate of the optimal solution for continuous optimization and Markov chains approach for combinatorial optimization. In the later case we show almost surely convergence of our algorithm to the optimal solution. Supporting numerical results for both continuous and combinatorial optimization problems are given as well. Our empirical studies suggest that the cross-entropy method has polynomial in the size of the problem running time complexity.
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    Integral equations and operator theory 35 (1999), S. 125-171 
    ISSN: 1420-8989
    Keywords: Primary 46L60 ; 47D25 ; 42A16 ; 43A65 ; Secondary 46L45 ; 42A65 ; 41A15
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    Topics: Mathematics
    Notes: Abstract This paper is devoted to an approximation problem for operators in Hilbert space, that appears when one tries to study geometrically thecascade algorithm in wavelet theory. Let $$\mathcal{H}$$ be a Hilbert space, and let π be a representation ofL ∞( $$\mathbb{T}$$ ) on $$\mathcal{H}$$ . LetR be a positive operator inL ∞( $$\mathbb{T}$$ ) such thatR(1) =1, where1 denotes the constant function 1. We study operatorsM on $$\mathcal{H}$$ (bounded, but noncontractive) such that $$\pi (f){\rm M} = M\pi (f(z^2 ))andM*\pi (f)M = \pi (R*f),f \in L^\infty (\mathbb{T}),$$ where the * refers to Hilbert space adjoint. We give a complete orthogonal expansion of $$\mathcal{H}$$ which reduces π such thatM acts as a shift on one part, and the residual part is $$\mathcal{H}$$ (∞) = ∩ n [M n $$\mathcal{H}$$ ], where [M n $$\mathcal{H}$$ ] is the closure of the range ofM n . The shift part is present, we show, if and only if ker (M *)≠{0}. We apply the operator-theoretic results to the refinement operator (or cascade algorithm) from wavelet theory. Using the representation π, we show that, for this wavelet operatorM, the components in the decomposition are unitarily, and canonically, equivalent to spacesL 2(E n ) ⊂L 2(ℝ), whereE n ⊂ ℝ, n=1,2,3,..., ∞, are measurable subsets which form a tiling of ℝ; i.e., the union is ℝ up to zero measure, and pairwise intersections of differentE n 's have measure zero. We prove two results on the convergence of the cascale algorithm, and identify singular vectors for the starting point of the algorithm.
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    ISSN: 1436-4646
    Keywords: 90C27 ; 68Q10 ; 68R05 ; Parallel computer ; MIMD ; branch and bound ; nondeterminism ; asynchronicity ; simulation
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    Topics: Computer Science , Mathematics
    Notes: Abstract Parallel computation offers a challenging opportunity to speed up the time consuming enumerative procedures that are necessary to solve hard combinatorial problems. Theoretical analysis of such a parallel branch and bound algorithm is very hard and empirical analysis is not straightforward because the performance of a parallel algorithm cannot be evaluated simply by executing the algorithm on a few parallel systems. Among the difficulties encountered are the noise produced by other users on the system, the limited variation in parallelism (the number of processors in the system is strictly bounded) and the waste of resources involved: most of the time, the outcomes of all computations are already known and the only issue of interest is when these outcomes are produced. We will describe a way to simulate the execution of parallel branch and bound algorithms on arbitrary parallel systems in such a way that the memory and cpu requirements are very reasonable. The use of simulation has only minor consequences for the formulation of the algorithm.
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    Mathematical programming 42 (1988), S. 33-40 
    ISSN: 1436-4646
    Keywords: Decision theory ; mathematical modelling ; operational research ; simulation
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    Topics: Computer Science , Mathematics
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    Meccanica 30 (1995), S. 105-124 
    ISSN: 1572-9648
    Keywords: Artificial ground motion ; probabilistic models ; random processes ; simulation ; earthquake engineering
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    Topics: Mechanical Engineering, Materials Science, Production Engineering, Mining and Metallurgy, Traffic Engineering, Precision Mechanics , Physics
    Description / Table of Contents: Sommario Sono analizzati criticamente i modelli probabilistici del moto sismico. Tale rassegna comprende processi modulati uniformemente, oscillatori, modulati in ampiezza e fase, modelli ARMA, ed altri. Inoltre, viene presentato un modello gaussiano non-stazionario che risulta innovativo e di validità generale. Il modello consiste nella sovrapposizione di armoniche con ampiezze gaussiane correlate. Le frequenze delle armoniche e le caratteristiche probabilistiche delle ampiezze dipendono rispettivamente dalla durata e dalla correlazione del moto sismico di riferimento. Il modello può essere generalizzato per rappresentare il moto sismico in due o più siti. Sono anche presentati alcuni metodi per la generazione di campioni artificiali del moto sismico. Tali metodi sono inoltre applicati alla generazione di sismi artificiali e alla valutazione dell'efficienza dei vari modelli probabilistici.
    Notes: Abstract Probabilistic models of seismic ground acceleration are reviewed. The review includes uniformly modulated, oscillatory, amplitude and phase modulated, ARMA, and other processes. Moreover, a novel and general nonstationary Gaussian model is presented. The model consists of a superposition of harmonics with correlated Gaussian amplitudes. The harmonic frequencies and the amplitude probabilistic characteristics depend on the duration and the correlation of the target seismic ground motion, respectively. The model can be generalized to represent the seismic ground motion at two or more sites. Methods are also presented for generating realizations of the probabilistic models in the paper. The methods are applied to demonstrate the generation of artificial seismic ground motions and to evaluate the usefulness of various probabilistic models in earthquake engineering.
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    Journal of intelligent and robotic systems 17 (1996), S. 309-325 
    ISSN: 1573-0409
    Keywords: modeling ; camera ; CCD ; subpixel ; simulation ; vision ; image ; diffusion ; CAD ; CIM ; bias
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    Topics: Computer Science , Mechanical Engineering, Materials Science, Production Engineering, Mining and Metallurgy, Traffic Engineering, Precision Mechanics
    Notes: Abstract In this paper we propose a modeling of an acquisition line made up of a CCD camera, a lens and a frame grabber card. The purpose of this modeling is to simulate the acquisition process in order to obtain images of virtual objects. The response time has to be short enough to permit interactive simulation. All the stages are modelised: in the first phase, we present a geometric model which supplies a point to point transformation that provides, for a space point in the camera field, the corresponding point on the plane of the CCD sensor. The second phase consists of modeling the discrete space which implies passing from the continous known object view to a discrete image, in accordance with the different orgin of the contrast loss. In the third phase, the video signal is reconstituted in order to be sampled by the frame grabber card. The practical results are close to reality when compared to image processing. This tool makes it possible to obtain a short computation time simulation of a vision sensor. This enables interactivity either with the user or with software for the design/simulation of an industrial workshop equipped with a vision system. It makes testing possible and validates the choice of sensor placement and image processing and analysis. Thanks to this simulation tool, we can control perfectly the position of the object image placed under the camera and in this way, we can characterise the performance of subpixel accuracy determining methods for object positioning.
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    Journal of intelligent and robotic systems 24 (1999), S. 125-149 
    ISSN: 1573-0409
    Keywords: planning ; control ; multi-fingered robot hand ; optimization ; internal force ; simulation
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    Topics: Computer Science , Mechanical Engineering, Materials Science, Production Engineering, Mining and Metallurgy, Traffic Engineering, Precision Mechanics
    Notes: Abstract In this paper, the problem of controlling multi-fingered robot hands with rolling and sliding contacts is addressed. Several issues are explored. These issues involve the kinematic analysis and modeling, the dynamic analysis and control, and the coordination of a multi-fingered robot hand system. Based on a hand-object system in which the contacts are allowed to both roll and slide, a kinematic model is derived and analyzed. Also, the dynamic model of the hand-object system with relative motion contacts is studied. A control law is proposed to guarantee the asymptotic tracking of the object trajectory together with the desired rolling and/or sliding motions along the surface of the object. A planning approach is then introduced to minimize the contact forces so that the desired motion of the object and the relative motions between the fingers and the object can be achieved. Simulation results which support the theoretical development are presented.
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    Numerische Mathematik 47 (1985), S. 191-215 
    ISSN: 0945-3245
    Keywords: AMS(MOS): 30B70 ; 40A15 ; 41A15 ; CR: G1.2
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    Topics: Mathematics
    Notes: Summary For continued fractionsK(a n /1) the concept of limit region is discussed, and its use for obtaining modified truncation error estimates is illustrated on examples. A certain strategy for numerical computation of limit regions is presented and illustrated on examples.
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    Applicable algebra in engineering, communication and computing 6 (1995), S. 211-243 
    ISSN: 1432-0622
    Keywords: Fundamental principle ; Injective cogenerator ; Multidimensional system ; Multivariate spline ; Locally finite sequence ; Polynomial exponential function ; 39A10 ; 13C11 ; 41A15 ; 93C35
    Source: Springer Online Journal Archives 1860-2000
    Topics: Computer Science , Mathematics , Technology
    Notes: Abstract New and known spaces of locally finite or polynomial exponential multivariate sequences and functions are constructed by means of substantial theorems from Commutative Algebra. They satisfy Ehrenpreis'fundamental principle and hence permit the solution of linear systems of partial differential or difference equations with constant coefficients. On the one hand this paper thus continues the author's work on multidimensional linear systems, on the other hand it generalizes and improves related work in approximation theory.
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    Acta mechanica solida Sinica 10 (1997), S. 283-298 
    ISSN: 0894-9166
    Keywords: fracture mechanics ; finite element ; simulation ; curved beam ; pipeline ; arrest
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    Topics: Mechanical Engineering, Materials Science, Production Engineering, Mining and Metallurgy, Traffic Engineering, Precision Mechanics , Physics
    Notes: Abstract Mechanical arrestors are frequently used in gas transmission pipelines to prevent the possibility of long running cracks. These arrestors have the effect of reducing the pipe from opening as the crack passes. This decreases the available crack driving force and, as a result, crack arrest may take place. This essentially is a second line of defence against catastrophic failure in the event crack initiation cannot always be prevented. A novel analyzing method presented in this paper has been developed to investigate the suitability of these crack arrestors. This is based on a fluid/structure/fracture interaction package, PFRAC. A dynamic finite element approach has been developed for a three dimension curved beam with initial plane curvature, which has been implemented in PFRAC to simulate the behaviour of the arrestor. The contact conditions between the pipe wall and the arrestor, along with the various computational procedures, are described. Several numerical results for a cracked pipe with arrestors are presented and compared with those for pipes without arrestors.
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    Numerische Mathematik 48 (1986), S. 323-336 
    ISSN: 0945-3245
    Keywords: AMS(MOS): 65L05 ; 65L07 ; 65D07 ; 65D10 ; 41A15 ; CR: G.1.7 ; G.1.2
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    Topics: Mathematics
    Notes: Summary In this paper non-linear splines (depending onn+1 parameters) are used to patch up the solution of an initial value problem in intervals of stepsizeh. The elements of the solution are fixed byq smoothness conditions andd conditions derived from the differential equation in an appropriate setup. The feasibility of the method can be connected to that of the polynomial spline method by a perturbation type argument. Thus the question of convergence forh→0 is closely connected to the linear (polynomial) case. A new elementary prove is given for divergence of the polynomial splines ifq is larger thand+1, as was done by Mülthei [4] with other techniques. A byproduct is an extention of the famous result for polynomial interpolation by Runge on equidistant grids that interpolation of a given function by splines of too high smoothness can cause divergence forh→0.
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    Finance and stochastics 1 (1996), S. 25-41 
    ISSN: 1432-1122
    Keywords: Key words: Martingale estimating function ; option pricing ; quasi-likelihood ; simulation ; stochastic differential equation ; volatility. ; JEL classification: G12 ; Mathematics Subject Classification (1991): 62M05
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics , Economics
    Notes: Abstract. In the present paper we consider a model for stock prices which is a generalization of the model behind the Black–Scholes formula for pricing European call options. We model the log-price as a deterministic linear trend plus a diffusion process with drift zero and with a diffusion coefficient (volatility) which depends in a particular way on the instantaneous stock price. It is shown that the model possesses a number of properties encountered in empirical studies of stock prices. In particular the distribution of the adjusted log-price is hyperbolic rather than normal. The model is rather successfully fitted to two different stock price data sets. Finally, the question of option pricing based on our model is discussed and comparison to the Black–Scholes formula is made. The paper also introduces a simple general way of constructing a zero-drift diffusion with a given marginal distribution, by which other models that are potentially useful in mathematical finance can be developed.
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    Constructive approximation 12 (1996), S. 409-422 
    ISSN: 1432-0940
    Keywords: 41A10 ; 41A15 ; 41A17 ; 41A25 ; 41A29 ; Degree of convex approximation ; Constrained approximation inL p space ; Spline approximation ; Polynomial approximation
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Abstract We prove that a convex functionf ∈ L p[−1, 1], 0〈p〈∞, can be approximated by convex polynomials with an error not exceeding Cω 3 ϕ (f,1/n)p where ω 3 ϕ (f,·) is the Ditzian-Totik modulus of smoothness of order three off. We are thus filling the gap between previously known estimates involving ω 3 ϕ (f,1/n)p, and the impossibility of having such estimates involving ω4. We also give similar estimates for the approximation off by convexC 0 andC 1 piecewise quadratics as well as convexC 2 piecewise cubic polynomials.
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  • 83
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    Constructive approximation 12 (1996), S. 127-155 
    ISSN: 1432-0940
    Keywords: 41A15 ; 42A38 ; 65D07 ; 65T10 ; B-splines with multiple knots ; Two-scale symbol ; Autocorrelation symbol ; Riesz basis ; Spline wavelets with multiple knots
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    Topics: Mathematics
    Notes: Abstract A generalized multiresolution of multiplicityr, generated byr linearly independent spline functions with multiple knots, is introduced. With the help of the autocorrelation symbol and the two-scale symbol of the scaling functions, spline wavelets with multiple knots can be completely characterized. New decomposition and reconstruction algorithms, based on the Fourier technique, are presented.
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    Constructive approximation 1 (1985), S. 137-154 
    ISSN: 1432-0940
    Keywords: 41A15 ; 41A5 ; 41A65 ; Perfect splines ; Monosplines ; Extended totally positive kernels ; Monotone norms ; Optimal quadrature formulas ; Optimal interpolation ; N-widths ; Optimal spaces
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    Topics: Mathematics
    Notes: Abstract Generalized monosplines of least norm are shown to exist and to determine optimal approximation processes such as numerical integration, interpolation and best approximating spaces. This extends various classical results related to monosplines and perfect splines, which are particular cases of generalized monosplines. The analysis here also provides for a unified treatment of the two classical classes of monosplines and perfect splines of least norm, and of their extremal properties.
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  • 85
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    Constructive approximation 1 (1985), S. 305-322 
    ISSN: 1432-0940
    Keywords: 41A15 ; Box spline ; Convergence rate ; Subdivision algorithms ; Control net
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    Topics: Mathematics
    Notes: Abstract Dahmen and Micchelli [8] have shown that in general the coefficients of the refined control nets of a box spline surface converge to the surface at (at least) the rate of the refinement. The purpose of this article is to show that under mild additional assumptions the convergence rate is even quadratic. Although this rate is in general best possible, we point out under what circumstances even higher rates are obtained (locally).
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  • 86
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    Constructive approximation 2 (1986), S. 79-99 
    ISSN: 1432-0940
    Keywords: 41A15 ; 41A52 ; 41A55 ; Monosplines ; Perfect splines ; L p-Approximation ; Uniqueness of best approximation ; Degree theory
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Abstract The uniqueness of monosplines and perfect splines of leastL p-norm is treated in the framework of generalized monosplines and total positivity. The analysis is based on the invariance properties of the degree of a certain mapping and on a new composition result for totally positive kernels. For theL p-case 1〈p〈∞, uniqueness is shown under the same extra conditions as were previously shown to be needed in theL p-case. The uniqueness in theL ∞-case is obtained without any restrictions.
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  • 87
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    Constructive approximation 2 (1986), S. 129-151 
    ISSN: 1432-0940
    Keywords: 41A05 ; 41A15 ; 41A29 ; Spline ; Constrained interpolation ; Smoothing ; Convexity preservation ; shape preservation
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Abstract Numerical and theoretical questions related to constrained interpolation and smoothing are treated. The prototype problem is that of finding the smoothest convex interpolant to given univariate data. Recent results have shown that this convex programming problem with infinite constraints can be recast as a finite parametric nonlinear system whose solution is closely related to the second derivative of the desired interpolating function. This paper focuses on the analysis of numerical techniques for solving the nonlinear system and on the theoretical issues that arise when certain extensions of the problem are considered. In particular, we show that two standard iteration techniques, the Jacobi and Gauss-Seidel methods, are globally convergent when applied to this problem. In addition we use the problem structure to develop an efficient implementation of Newton's method and observe consistent quadratic convergence. We also develop a theory for the existence, uniqueness, and representation of solutions to the convex interpolation problem with nonzero lower bounds on the second derivative (strict convexity). Finally, a smoothing spline analogue to the convex interpolation problem is studied with reference to the computation of convex approximations to noisy data.
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    Constructive approximation 3 (1987), S. 31-42 
    ISSN: 1432-0940
    Keywords: Splines with free knots ; Best approximation ; Supremum norm ; Strong unicity ; Alternation conditions ; 41A15 ; 41A52
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Abstract A necessary and a sufficient alternation condition for strongly unique best spline approximations with free knots is given. In the case of simple knots these conditions coincide, and strongly unique best approximations and strongly unique local best approximations are the same. The numerical consequences are discussed.
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  • 89
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    Constructive approximation 3 (1987), S. 123-130 
    ISSN: 1432-0940
    Keywords: Bernstein-Schoenberg operator ; Bernstein polynomial ; MultivariateB-spline ; Asymptotic error ; 41A15 ; 41A63
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Abstract The bivariate Bernstein-Schoenberg operatorV T of degreem, introduced in [5], is a spline approximation operator that generalizes the Bernstein polynomial operatorB m . It is shown here that for a convex functionf,f≤V T (f)≤B m (f). This result is then used to show that for a twice differentiable functiong, the asymptotic error limm(V T (g)-g) depends only on the asymptotic error for quadratic polynomials. The latter is evaluated explicitly in the special circumstances thatV T is, in a sense, asymptotically close toB m .
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  • 90
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    Constructive approximation 3 (1987), S. 143-156 
    ISSN: 1432-0940
    Keywords: Divided differences ; Hyperbolic equations ; Lifting distributions ; Interpolation ; B-splines ; 41A15 ; 41A63 ; 41A05 ; 35A08
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Abstract We discuss the relationship between divided differences, fundamental functions of hyperbolic equations, multivariate interpolation, and polyhedral splines.
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  • 91
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    Constructive approximation 3 (1987), S. 111-122 
    ISSN: 1432-0940
    Keywords: Box splines ; Commutator ; Marsden's identity ; Quasi-interpolation ; 41A15 ; 41A63
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Abstract Let ϕ be a linear combination of certain box splines and $$\hat \phi $$ its Fourier transform, such that $$\hat \phi \left( 0 \right) \ne 0$$ and $$D^\beta \hat \phi \left( {2\pi k} \right) = 0$$ for all κ∈ZN{0} and β≤α. In this paper we construct an expression of the multivariate polynomial (·-y)α in terms of a linear combination of the integer translates of ϕ(·), where the coefficients can be computed recursively using only the information on $$D^\beta \hat \phi \left( 0 \right)$$ , β ≤ α. As an application, a quasi-interpolation scheme based only on function values on (scaled) integers κ∈ZN is constructed that gives a “multivariate order” of approximation that includes both coordinate and total orders.
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    Constructive approximation 3 (1987), S. 169-188 
    ISSN: 1432-0940
    Keywords: Cardinal interpolation ; Box splines ; 4-Direction mesh ; Primary 41A05 ; 41A15 ; Secondary 41A63
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Abstract This paper introduces the idea of cardinal interpolation on submodules of Zd by translates of box splines if the condition of global linear independence fails to hold. In particular, the special case of the 4-direction box splines is discussed, where the pertinent submodule is given by the pairs (k, l) of integersk, l withk+l even. For this case, one obtains results that parallel the known results for the 3-direction box splines.
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    Constructive approximation 3 (1987), S. 131-141 
    ISSN: 1432-0940
    Keywords: Multivariate cone and simplex splines ; Surfaces ; Approximation ; Algorithms ; Computation ; Spatial dimension ; 41A15 ; 41A63 ; 65D07
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Abstract We prove some new relations between functions defined as shadows of cones (cone splines) and simplices (simplex splines). We use them to show how ans-variate simplex spline of some orderk can be written as a sum ofk+1 (s-l)-variate simplex splines of orderk-1. A recurrence relation on the spatial dimension of the simplex spline,s, is proposed as an interesting alternative to the recurrence relation in [17], where one uses the orderk for recursion, but not the spatial dimensions.
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    Constructive approximation 3 (1987), S. 189-197 
    ISSN: 1432-0940
    Keywords: Multivariate splines ; Splines ; Piecewise polynomial functions ; Triangulations ; Primary 65D07 ; Secondary 41A63 ; 41A15
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Abstract We consider spaces of piecewise polynomials of degreed defined over a triangulation of a polygonal domain and possessingr continuous derivatives globally. Morgan and Scott constructed a basis in the case wherer=1 andd≥5. The purpose of this paper is to extend the dimension part of their result tor≥0 andd≥4r+l. We use Bézier nets as a crucial tool in deriving the dimension of such spaces.
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  • 95
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    Constructive approximation 3 (1987), S. 209-221 
    ISSN: 1432-0940
    Keywords: Discrete box splines ; Discrete truncated powers ; Linear independence ; Piecewise structure ; Number of solutions to linear diophantine equations ; 41A15 ; 41A63 ; 39A70 ; 10B30 ; 10A21 ; 10A50 ; 05B35
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Abstract The central objective of this paper is to discuss linear independence of translates of discrete box splines which we introduced earlier as a device for the fast computation of multivariate splines. The results obtained here allow us to draw conclusions about the structure of such discrete splines which have, in particular, applications to counting the number of nonnegative integer solutions of linear diophantine equations.
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  • 96
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    Constructive approximation 3 (1987), S. 199-208 
    ISSN: 1432-0940
    Keywords: Box splines ; Multivariate ; Splines ; Quasi-interpolant ; Semidiscrete convolution ; 41A15 ; 41A63 ; 41A25
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Abstract Algebraic facts about the space of polynomials contained in the span of integer translates of a compactly supported function are derived and then used in a discussion of the various quasi-interpolants from that span.
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    Constructive approximation 3 (1987), S. 223-238 
    ISSN: 1432-0940
    Keywords: Interpolation ; Cardinal interpolation ; Hermite interpolation ; Box splines ; Primary 41A05 ; 41A15 ; Secondary 41A63
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Abstract The study of cardinal interpolation (CIP) by the span of the lattice translates of a box spline has met with limited success. Only the case of interpolation with the box spline determined by the three directionsd 1=(1, 0),d 2=(0, 1), andd 3=(1, 1) inR 2 has been treated in full generality [2]. In the case ofR d,d ≥ 3, the directions that define the box spline must satisfy a certain determinant condition [6], [9]. If the directions occur with even multiplicities, then this condition is also sufficient. For Hermite interpolation (CHIP) both even multiplicities and the determinant condition for the directions does not prevent the linear dependence of the basis functions. This leads to singularities in the characteristic multiplier when using the standard Fourier transform method. In the case of derivatives in one direction, these singularities can be removed and a set of fundamental splines can be given. This gives the existence of a solution to CHIP inL p (R d) for data inl p (Z d), 1≤p≤2.
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    Constructive approximation 3 (1987), S. 363-375 
    ISSN: 1432-0940
    Keywords: Splines of least norm ; Perfect splines ; Mono splines ; Multiple zeros ; 41A15 ; 41A29 ; 41A52
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Abstract LetP(N,m;r 1,...,r n ) be the class of 1-periodic perfect splines of degreem with 2N knots, which haven distinct zeros in one period with multiplicitiesr 1,...,r n , respectively. We show that there exists a unique extremal elementP *∈P(N,m;r 1,...,r n ) of minimal uniform norm which equioscillates. This problem is related to the optimal recovery of smooth periodic functions on the basis of the Hermitian data.
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    Constructive approximation 4 (1988), S. 1-7 
    ISSN: 1432-0940
    Keywords: 41A15 ; 41A05 ; Spline interpolation ; Knot averages ; Geometric mesh
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Abstract It is well known that when interpolation points coincide with knots, the knot sequence must obey some restriction in order to guarantee the existence and boundedness of the interpolation projector. But, when the interpolation points are chosen to be the knot averages, the corresponding quadratic or cubic spline interpolation projectors are bounded independently of the knot sequence. Based on this fact, de Boor in 1975 made a conjecture that interpolation by splines of orderk at knot averages is bounded for anyk. In this paper we disprove de Boor's conjecture fork ⩾ 20.
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    Constructive approximation 4 (1988), S. 133-145 
    ISSN: 1432-0940
    Keywords: 41A05 ; 41A15 ; 65D05 ; 65D07 ; Generalized spline spaces ; B-splines ; Weak Descartes systems ; Weak Tchebycheffian subspaces
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Abstract A class of generalized spline spaces is introduced for which a basis of functions with local support is constructed by using a recursion relation. It is shown that this basis forms a weak Descartes system. Moreover, an interpolation property is given.
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