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  • Chebyshev
  • numerical methods
  • 2020-2023
  • 2010-2014
  • 1995-1999  (2)
  • 1970-1974  (4)
  • 1965-1969
  • 1935-1939
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  • 1
    Electronic Resource
    Electronic Resource
    Error estimates of Hermite interpolation (1973)
    Springer
    BIT 13 (1973), S. 338-343 
    Details
    ISSN: 1572-9125
    Keywords: Hermite interpolation ; Chebyshev ; order of continuity
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Abstract This paper presents a procedure for obtaining error estimates for Hermite interpolation at the Chebyshev nodes {cos ((2j+1)π/2n)} j =0n−1 −1≦x≦1, for functionsf(x) of various orders of continuity. The procedure is applicable in many cases when the usual Lagrangian error bound is not, and is a better bound, in general, when both are applicable.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF01951944
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  • 2
    Electronic Resource
    Electronic Resource
    A second-order iterative technique for differential-integral systems (1974)
    Springer
    Journal of optimization theory and applications 13 (1974), S. 179-185 
    Details
    ISSN: 1573-2878
    Keywords: Optimal control theory ; functional differential equations ; numerical methods ; hereditary processes ; contraction mapping principle
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Abstract This note considers the optimal control of a system represented by nonlinear differential-integral equations with a general cost function. A second-order iterative method of solution based on the fixed-point contraction mapping principle is proposed.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF00935538
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  • 3
    Electronic Resource
    Electronic Resource
    Parameter variation for the solution of two-point boundary-value problems and applications in the calculus of variations (1974)
    Springer
    Journal of optimization theory and applications 13 (1974), S. 164-178 
    Details
    ISSN: 1573-2878
    Keywords: Two-point boundary-value problems ; calculus of variations ; numerical methods ; differential equations ; computing methods
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Abstract In the parameter variation method, a scalar parameterk, kε[0, 1], is introduced into the differential equations. The parameterk is inserted in such a way that, whenk=0, the solution of the boundary-value problem is known or readily calculated and, whenk=1, the problem is identical with the original problem. Thus, bydeforming the solution step-by-step throughk-space fromk=0 tok=1, the original problem may be solved. These solutions then provide good starting values for any convergent, iterative scheme such as the Newton-Raphson method. The method is applied to the solution of problems with various types of boundary-value specifications and is further extended to take account of situations arising in the solution of problems from variational calculus (e.g., total elapsed time not specified, optimum control not a simple function of the variables).
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF00935537
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  • 4
    Electronic Resource
    Electronic Resource
    An assessment of residual-stress measurements around cold-worked holes (1995)
    Springer
    Experimental mechanics 35 (1995), S. 361-366 
    Details
    ISSN: 1741-2765
    Keywords: finite elements ; stress-strain of material behaviors ; nondestructive testing ; numerical methods ; plasticity ; residual stresses ; X-ray analysis
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mechanical Engineering, Materials Science, Production Engineering, Mining and Metallurgy, Traffic Engineering, Precision Mechanics
    Notes: Abstract An X-ray diffraction technique was employed to determine the residual stresses introduced by cold working a fastener hole in a 6-mm thick 2024-T351 aluminum plate. The radial and tangenital residual stresses were measured at both faces of the plate and the measurements compared with the results from a two-dimensional axisymmetric finite-element model. The comparisons were favorable, although modifying the finite-element model to simulate the X-ray process provided better agreement. Experimental determinations of residual stresses showed differences between the two faces of the plate. This feature was attributed to the directional nature of the cold-working process.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF02317546
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  • 5
    Electronic Resource
    Electronic Resource
    Decomposition technique for minimum time trajectories (1974)
    Springer
    Journal of optimization theory and applications 14 (1974), S. 233-250 
    Details
    ISSN: 1573-2878
    Keywords: Time-optimal control ; decomposition methods ; two-point boundary-value problems ; trajectories ; numerical methods
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Abstract A decomposition technique is presented for minimum-time trajectories which are characterized by intermediate constraints and discontinuities. The optimization of such multiple are trajectories is usually a formidable task. One optimization method, trajectory decomposition, breaks the original trajectory at points of discontinuity into separate arcs and then optimizes each are subject to prescribed boundary conditions. This constitutes a first level of control. Each first-level solution is evaluated by a second-level controller, which iteratively specifies new are boundary conditions in order to achieve an optimum solution. Unfortunately, this two-level method cannot be applied directly to minimum-time trajectories. The two-level trajectory decomposition method is extended here to a three-level technique for treating the minimum-time trajectory. The first level again optimizes each are for specified intervention parameters. The new second level, the time interface controller, exploits certain homogeneity properties to satisfy time transversality conditions at all boundaries and to couple the first-level solution arcs in time. The third level, the state interface controller, satisfies state transversality conditions at the arc junctions iteratively while driving the trajectory to its optimum. The new three-level procedure represents a feasible decomposition because each solution trajectory in the iterative sequence is physically realizable. The technique also offers a decentralization of control effort and reduction of initial-value sensitivities. An example problem is formulated.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF00932942
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  • 6
    Electronic Resource
    Electronic Resource
    Numerical methods for analyzing the effects of uncertainties on the dynamics of periodic structures (1997)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 40 (1997), S. 3749-3765 
    Details
    ISSN: 0029-5981
    Keywords: localization ; disorders ; numerical methods ; periodic structures ; Engineering ; Numerical Methods and Modeling
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: Various approaches are proposed and compared for analysing the effects of structural irregularities and parameter uncertainties on the dynamics of finitely long, one-dimensional, mono-coupled, nearly periodic assemblies with and without structural damping. Computational concerns are raised in regard to the classical method of modal analysis, and alternative methods are formulated which allow for the numerically efficient determination of the exponential decay constant. While modal analysis and Cramer's rule require the solution of an eigenvalue problem, the matrix inversion and matrix partitioning approaches avoid costly eigenvalue computations and require only cost-effective algebraic manipulations. Therefore, implementation of either the direct inversion technique or matrix partitioning both simplifies the analysis and cuts computational costs substantially. © 1997 John Wiley & Sons, Ltd.
    Additional Material: 9 Ill.
    Type of Medium: Electronic Resource
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