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  • 1
    Digitale Medien
    Digitale Medien
    Springer
    Mathematical programming 22 (1982), S. 163-201 
    ISSN: 1436-4646
    Schlagwort(e): Geometric Programming ; Code Comparisons ; Numerical Testing ; Nonlinear Programming
    Quelle: Springer Online Journal Archives 1860-2000
    Thema: Informatik , Mathematik
    Notizen: Abstract Ten codes or code variants were used to solve the five equivalent posynomial GP problem formulations. Four of these codes were general NLP codes; six were specialized GP codes. A total of forty-two test problems was solved with up to twenty randomly generated starting points per problem. The convex primal formulation is shown to be intrinsically easiest to solve. The general purpose GRG code called OPT appears to be the most efficient code for GP problem solution. The reputed superiority of the specialized GP codes GGP and GPKTC appears to be largely due to the fact that these codes solve the convex primal formulation. The dual approaches are only likely to be competitive for small degree of difficulty, tightly constrained problems.
    Materialart: Digitale Medien
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  • 2
    Digitale Medien
    Digitale Medien
    Springer
    Mathematical programming 23 (1982), S. 75-86 
    ISSN: 1436-4646
    Schlagwort(e): Constrained Optimization ; Global Convergence ; Nonlinear Programming ; Penalty Function ; Quasi-Newton Method
    Quelle: Springer Online Journal Archives 1860-2000
    Thema: Informatik , Mathematik
    Notizen: Abstract The recently proposed quasi-Newton method for constrained optimization has very attractive local convergence properties. To force global convergnce of the method, a descent method which uses Zangwill's penalty function and an exact line search has been proposed by Han. In this paper a new method which adopts a differentiable penalty function and an approximate line is presented. The proposed penalty function has the form of the augmented Lagrangian function. An algorithm for updating parameters which appear in the penalty function is described. Global convergence of the given method is proved.
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  • 3
    Digitale Medien
    Digitale Medien
    Springer
    Mathematical programming 22 (1982), S. 82-92 
    ISSN: 1436-4646
    Schlagwort(e): Generic Programming ; Optimality Conditions ; Nonlinear Programming
    Quelle: Springer Online Journal Archives 1860-2000
    Thema: Informatik , Mathematik
    Notizen: Abstract Optimality conditions for families of nonlinear programming problems inR n are studied from a generic point of view. The objective function and some of the constraints are assumed to depend on a parameter, while others are held fixed. Techniques of differential topology are used to show that under suitable conditions, certain strong second-order conditions are necessary for optimality except possibly for parameter values lying in a negligible set.
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  • 4
    Digitale Medien
    Digitale Medien
    Springer
    Mathematical programming 24 (1982), S. 137-161 
    ISSN: 1436-4646
    Schlagwort(e): Nonlinear Programming ; Exact Penalty Methods ; Successive Quadratic Programming
    Quelle: Springer Online Journal Archives 1860-2000
    Thema: Informatik , Mathematik
    Notizen: Abstract In this paper we motivate and describe an algorithm to solve the nonlinear programming problem. The method is based on an exact penalty function and possesses both global and superlinear convergence properties. We establish the global qualities here (the superlinear nature is proven in [7]). The numerical implementation techniques are briefly discussed and preliminary numerical results are given.
    Materialart: Digitale Medien
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  • 5
    Digitale Medien
    Digitale Medien
    Springer
    Numerische Mathematik 40 (1982), S. 47-56 
    ISSN: 0945-3245
    Schlagwort(e): AMS (MOS): 65F30 ; CR: 5.14
    Quelle: Springer Online Journal Archives 1860-2000
    Thema: Mathematik
    Notizen: Summary Fast Givens rotations with half as many multiplications are proposed for orthogonal similarity transformations and a matrix notation is introduced to describe them more easily. Applications are proposed and numerical results are examined for the Jacobi method, the reduction to Hessenberg form and the QR-algorithm for Hessenberg matrices. It can be seen that in general fast Givens rotations are competitive with Householder reflexions and offer distinct advantages for sparse matrices.
    Materialart: Digitale Medien
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  • 6
    Digitale Medien
    Digitale Medien
    Springer
    Numerische Mathematik 40 (1982), S. 137-141 
    ISSN: 0945-3245
    Schlagwort(e): (MR 1980) AMS(MOS) ; 65F05, 15A06, 10M10, 10A30 ; CR: 5.14
    Quelle: Springer Online Journal Archives 1860-2000
    Thema: Mathematik
    Notizen: Summary A method is described for computing the exact rational solution to a regular systemAx=b of linear equations with integer coefficients. The method involves: (i) computing the inverse (modp) ofA for some primep; (ii) using successive refinements to compute an integer vector $$\bar x$$ such that $$A\bar x \equiv b$$ (modp m ) for a suitably large integerm; and (iii) deducing the rational solutionx from thep-adic approximation $$\bar x$$ . For matricesA andb with entries of bounded size and dimensionsn×n andn×1, this method can be implemented in timeO(n 3(logn)2) which is better than methods previously used.
    Materialart: Digitale Medien
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  • 7
    Digitale Medien
    Digitale Medien
    Springer
    Numerische Mathematik 40 (1982), S. 201-206 
    ISSN: 0945-3245
    Schlagwort(e): AMS(MOS): 65F05, 65F15, 65H10 ; CR: 5.14
    Quelle: Springer Online Journal Archives 1860-2000
    Thema: Mathematik
    Notizen: Summary In this paper, motivated by Symm-Wilkinson's paper [5], we describe a method which finds the rigorous error bounds for a computed eigenvalue λ(0) and a computed eigenvectorx (0) of any matrix A. The assumption in a previous paper [6] that λ(0),x (0) andA are real is not necessary in this paper. In connection with this method, Symm-Wilkinson's procedure is discussed, too.
    Materialart: Digitale Medien
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  • 8
    Digitale Medien
    Digitale Medien
    Springer
    Mathematical programming 24 (1982), S. 123-136 
    ISSN: 1436-4646
    Schlagwort(e): Nonlinear Programming ; Exact Penalty Methods ; Successive Quadratic Programming
    Quelle: Springer Online Journal Archives 1860-2000
    Thema: Informatik , Mathematik
    Notizen: Abstract In this paper we consider the final stage of a ‘global’ method to solve the nonlinear programming problem. We prove 2-step superlinear convergence. In the process of analyzing this asymptotic behavior, we compare our method (theoretically) to the popular successive quadratic programming approach.
    Materialart: Digitale Medien
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  • 9
    Digitale Medien
    Digitale Medien
    Springer
    Applied physics 27 (1982), S. 167-169 
    ISSN: 1432-0630
    Schlagwort(e): 61.70 ; 68 ; 74
    Quelle: Springer Online Journal Archives 1860-2000
    Thema: Maschinenbau , Physik
    Notizen: Abstract A simple method is presented to prepare very low pinning niobium foils on which geometrically well defined Nb3Sn-pinning structures of arbitrary shape are deposited. This facilitates the fabrication of samples for guided vortex motion experiments some of which are reported.
    Materialart: Digitale Medien
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  • 10
    Digitale Medien
    Digitale Medien
    Springer
    Applied physics 28 (1982), S. 99-102 
    ISSN: 1432-0630
    Schlagwort(e): 61.70 ; 81.40
    Quelle: Springer Online Journal Archives 1860-2000
    Thema: Maschinenbau , Physik
    Notizen: Abstract Supersaturated surface alloys produced by very high dose (0.8−2.6×1017cm−2) implantation of As-ions into silicon and subsequent pulsed electron-beam annealing have been investigated by means of the channeling technique. The maximum solubility limit of 7×1021 As/cm3 has been determined. It exceeds the equilibrium solubility limit by more than a factor of 4. Angular scan measurements indicated that for doses above 1×1017cm−2 As atoms are displaced by about 0.12 Å from the regular lattice sites.
    Materialart: Digitale Medien
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  • 11
    Digitale Medien
    Digitale Medien
    Springer
    Applied physics 28 (1982), S. 179-187 
    ISSN: 1432-0630
    Schlagwort(e): 78.70 ; 61.70
    Quelle: Springer Online Journal Archives 1860-2000
    Thema: Maschinenbau , Physik
    Notizen: Abstract Positron annihilation measurements of the coincidence count rate at the peak of the angular correlation curve (CCR) have been performed as a function of temperature for the alloy systemFeTi in a concentration range up to about 1.3 at. %. The concentration dependence of the effective vacancy formation enthalpy (H 1V F )eff suggests the existence of an attractive interaction between vacancies and the impurity atoms. It will be shown that the description of the vacancy concentration in an alloy according to the Lomer model is not valid in this case, because it neglects binding of vacancies to solute atom pairs and to higher agglomerates. The application of a model proposed by Dorn and Mitchell gives evidence that beyond the binding of a vacancy to a single solute atom in the concentration range investigated also aggregates of a vacancy bound to two and three foreign atoms must be taken into account. The analysis of the measurements according to the method of Hehenkamp and Sander gives values for the respective vacancy-solute-atom(s) binding enthalpies H 1 B =0.25eV, H 2 B =0.53eV and H 3 B =0.91eV. The discussion of the temperature and solute-atoms concentration dependence of the vacancy concentration suggests a much more complicated behaviour than for pure metals even at low solute-atom concentrations.
    Materialart: Digitale Medien
    Standort Signatur Erwartet Verfügbarkeit
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  • 12
    Digitale Medien
    Digitale Medien
    Springer
    Applied physics 27 (1982), S. 257-261 
    ISSN: 1432-0630
    Schlagwort(e): 78.70 ; 61.70 ; 81
    Quelle: Springer Online Journal Archives 1860-2000
    Thema: Maschinenbau , Physik
    Notizen: Abstract The positron lifetime was measured in cadmium in the temperature range between 80 K and 500 K. For the first time a plateau was observed by this method in polycrystalline samples. The obtained data are well explained by depletion of shallow traps forT≤180 K and by self-trapping in the prevacancy region.
    Materialart: Digitale Medien
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  • 13
    Digitale Medien
    Digitale Medien
    Springer
    Applied physics 29 (1982), S. 105-111 
    ISSN: 1432-0630
    Schlagwort(e): 71.55F ; 61.70 ; 73.40Q
    Quelle: Springer Online Journal Archives 1860-2000
    Thema: Maschinenbau , Physik
    Notizen: Abstract The annealing behavior of trap-centers was studied in float-zone silicon wafers containing A-swirl defects. Samples from areas of high and low A-swirl density were annealed in nitrogen ambient between 100° and 900 °C, and analysed using the Deep Level Transient Spectroscopy. The results indicate, that two levels atE c }-0.07 eV,σ n=4.6×10−16 cm2, andE c−0.49eV,σ n=6.6×10−16cm2 are caused by one defect, for which the silicon di-selfinterstitial is a likely interpretation. A level atE c }-0.11 eV was assigned to interstitial carbon. Both defects annealed out at about 170 °C. After 600 °C annealing an additional level atE c−0.2 eV was detected, which was attributed to an interstitial silicon carbon complex. Heat treatment at 800 °C generated a new level atE c−0.49 eV,σ n=2.9×10−16cm2 only in the area of high A-swirl defect density. This level was also observed after oxidation and subsequent annealing of silicon.
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  • 14
    Digitale Medien
    Digitale Medien
    Springer
    Applied physics 27 (1982), S. 49-56 
    ISSN: 1432-0630
    Schlagwort(e): 61.70 ; 78.70
    Quelle: Springer Online Journal Archives 1860-2000
    Thema: Maschinenbau , Physik
    Notizen: Abstract Trapping of positrons at vacancy-type defects in magnesium was studied by positron lifetime and Doppler-broadening measurements. Vacancy defects were produced by quenching, electron irradiation and deformation at low temperatures as well as by thermal agitation at elevated temperatures. In the first three cases we observed trapping at multiple vacancies, which anneal out between 77...400 K. Thermal equilibrium measurements show S-shape behaviour originating from positron trapping at magnesium monovacancies. However, changes in the positron parameters were very small, which is due to the weakness of the positron-vacancy interaction. A detrapping analysis yielded a positron-vacancy binding energy of the order of 0.3...0.4 eV.
    Materialart: Digitale Medien
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  • 15
    ISSN: 1432-0630
    Schlagwort(e): 61.70 ; 78.70
    Quelle: Springer Online Journal Archives 1860-2000
    Thema: Maschinenbau , Physik
    Notizen: Abstract Positron-annihilation lineshape parameter measurements were performed during isothermal annealing of room temperature deformed iron. An isothermal annealing effect is seen in impure iron while in pure iron no effect is measured.
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  • 16
    Digitale Medien
    Digitale Medien
    Springer
    Applied physics 27 (1982), S. 149-152 
    ISSN: 1432-0630
    Schlagwort(e): 78.70 ; 61.70
    Quelle: Springer Online Journal Archives 1860-2000
    Thema: Maschinenbau , Physik
    Notizen: Abstract A simple model is developed for the trapping of positrons at grain boundaries. It is shown that there is a linear relationship between any linear annihilation parameter and the inverse grain size. An effective grain boundary width is defined, which depends on the positron diffusion length and on the strength of the grain boundary for positrons. The effect of detrapping on this effective width is also considered. The model is tested by using the experimental results available in the literature.
    Materialart: Digitale Medien
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  • 17
    Digitale Medien
    Digitale Medien
    Springer
    Applied physics 27 (1982), S. 171-176 
    ISSN: 1432-0630
    Schlagwort(e): 61.70 ; 66 ; 85.30
    Quelle: Springer Online Journal Archives 1860-2000
    Thema: Maschinenbau , Physik
    Notizen: Abstract The paper presents a theoretical study of the diffusion of gold into dislocated silicon wafers in terms of the kick-out mechanism Au i ⇄Au s +I, where Au i , Au s , andI mean Au interstitials, substitutional Au atoms, and Si self-interstitials, respectively. In agreement with experiments it is found that the Au s concentration in the centre of a wafer,C s m , increases with the durationt of the diffusion anneal according toC s m =C s eq (k 0 t)1/2 except forC s m values in the vicinity of the solubility limitC s eq of Au s . Approximate analytical expressions fork 0 as a function of the densityN I of the dislocations acting asI sinks are given for the entire regime 0≦NI〈+t8.
    Materialart: Digitale Medien
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  • 18
    Digitale Medien
    Digitale Medien
    Springer
    Applied physics 29 (1982), S. 199-200 
    ISSN: 1432-0630
    Schlagwort(e): 61.70
    Quelle: Springer Online Journal Archives 1860-2000
    Thema: Maschinenbau , Physik
    Notizen: Abstract Conditions are discussed under which an interstitial atom absorbed in the core of a gliding 60° dislocation belonging to the glide set can be transformed into an antisite defect. The mechanism considered may be responsible for an increase in the concentration of AsGa defects observed in GaAs single crystals after their plastic deformation.
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  • 19
    Digitale Medien
    Digitale Medien
    Springer
    Applied physics 28 (1982), S. 79-92 
    ISSN: 1432-0630
    Schlagwort(e): 61.70 ; 66.30 ; 85.30
    Quelle: Springer Online Journal Archives 1860-2000
    Thema: Maschinenbau , Physik
    Notizen: Abstract The information available on the diffusion of oxygen and on the formation of thermal donors in silicon is critically reviewed. In this context the effects of intrinsic point defects on the diffusion-controlled growth of oxygen precipitates is investigated in some detail. Seemingly contradictory experimental results on the diffusivity of oxygen in silicon at temperatures around 400° C are explained in terms offast-diffusing gas-like molecular oxygen in silicon. The concept of molecular oxygen is also invoked in a newly suggested model of thermal donor formation in silicon. The diffusivity of molecular oxygen in silicon is estimated to be around 10−9cm2s−1 at 450° C, almost nine orders of magnitude higher than the diffusivity of atomic oxygen in interstitial position.
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  • 20
    Digitale Medien
    Digitale Medien
    Springer
    Numerische Mathematik 40 (1982), S. 57-69 
    ISSN: 0945-3245
    Schlagwort(e): AMS(MOS): 65F05 ; CR: 5.14
    Quelle: Springer Online Journal Archives 1860-2000
    Thema: Mathematik
    Notizen: Summary Using the simple vehicle ofM-matrices, the existence and stability ofLU decompositions of matricesA which can be scaled to diagonally dominant (possibly singular) matrices are investigated. Bounds on the growth factor for Gaussian elimination onA are derived. Motivation for this study is provided in part by applications to solving homogeneous systems of linear equationsAx=0, arising in Markov queuing networks, input-output models in economics and compartmental systems, whereA or −A is an irreducible, singularM-matrix. This paper extends earlier work by Funderlic and Plemmons and by Varga and Cai.
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  • 21
    Digitale Medien
    Digitale Medien
    Springer
    Numerische Mathematik 40 (1982), S. 297-306 
    ISSN: 0945-3245
    Schlagwort(e): AMS (MOS): 65F25 ; CR: 5.14
    Quelle: Springer Online Journal Archives 1860-2000
    Thema: Mathematik
    Notizen: Summary This paper describes an algorithm for simultaneously diagonalizing by orthogonal transformations the blocks of a partitioned matrix having orthonormal columns.
    Materialart: Digitale Medien
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  • 22
    Digitale Medien
    Digitale Medien
    Springer
    Numerische Mathematik 38 (1982), S. 53-59 
    ISSN: 0945-3245
    Schlagwort(e): AMS(MOS): 65F10 ; 47B55 ; CR: 5.14
    Quelle: Springer Online Journal Archives 1860-2000
    Thema: Mathematik
    Notizen: Summary By means of successive partial substitutions it is possible to obtain new fixed point linear equations from old ones and it is interesting to determine how the spectral radius of the corresponding matrices varies. We prove that, when the original matrix is nonnegative, this variation is decreasing or increasing, depending on whether the original matrix has its spectral radius smaller or greater than 1. We answer in this way a question posed by F. Robert in [5].
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  • 23
    Digitale Medien
    Digitale Medien
    Springer
    Numerische Mathematik 38 (1982), S. 417-419 
    ISSN: 0945-3245
    Schlagwort(e): AMS(MOS): 65F10 ; CR: 5.14
    Quelle: Springer Online Journal Archives 1860-2000
    Thema: Mathematik
    Notizen: Summary A modification to the well known bisection algorithm [1] when used to determine the eigenvalues of a real symmetric matrix is presented. In the new strategy the terms in the Sturm sequence are computed only as long as relevant information on the required eigenvalues is obtained. The resulting algorithm usingincomplete Sturm sequences can be shown to minimise the computational work required especially when only a few eigenvalues are required. The technique is also applicable to other computational methods which use the bisection process.
    Materialart: Digitale Medien
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  • 24
    Digitale Medien
    Digitale Medien
    Springer
    Numerische Mathematik 39 (1982), S. 85-96 
    ISSN: 0945-3245
    Schlagwort(e): AMS65F05 ; 65F 15 ; 65F 20 ; 65F 35 ; CR: 5.14
    Quelle: Springer Online Journal Archives 1860-2000
    Thema: Mathematik
    Notizen: Summary In this paper the use of the condition number of a problem, as defined by Rice in 1966, is discussed. For the eigenvalue, eigenvector, and linear least squares problems either condition numbers according to various norms are determined or lower and upper bounds for them are derived.
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  • 25
    Digitale Medien
    Digitale Medien
    Springer
    Numerische Mathematik 38 (1982), S. 333-345 
    ISSN: 0945-3245
    Schlagwort(e): AMS(MOS): 15 A 09, 15-04 ; CR: 5.14
    Quelle: Springer Online Journal Archives 1860-2000
    Thema: Mathematik
    Notizen: Summary This paper presents a simple algorithm for inverting nonsymmetric tridiagonal matrices that leads immediately to closed forms when they exist. Ukita's theorem is extended to characterize the class of matrices that have tridiagonal inverses.
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  • 26
    Digitale Medien
    Digitale Medien
    Springer
    Numerische Mathematik 39 (1982), S. 113-117 
    ISSN: 0945-3245
    Schlagwort(e): AMS(MOS): 65F10 ; CR: 5.14
    Quelle: Springer Online Journal Archives 1860-2000
    Thema: Mathematik
    Notizen: Summary We prove that if the matrixA has the structure which results from the so-called “red-black” ordering and ifA is anH-matrix then the symmetric SOR method (called the SSOR method) is convergent for 0〈ω〈2. In the special case thatA is even anM-matrix we show that the symmetric single-step method cannot be accelerated by the SSOR method. Symmetry of the matrixA is not assumed.
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  • 27
    Digitale Medien
    Digitale Medien
    Springer
    Numerische Mathematik 39 (1982), S. 163-173 
    ISSN: 0945-3245
    Schlagwort(e): AMS(MOS): 65F10 ; CR: 5.14
    Quelle: Springer Online Journal Archives 1860-2000
    Thema: Mathematik
    Notizen: Summary Recently D.J. Evans introduced an implicit matrix inversion process showing asymptotic behaviour which is superior to that of the well known Schulz-method. In this paper we give sufficient conditions for convergence, prove some error bounds and show that under certain conditions the iterates are converging monotonously.
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