Chebyshev Multivariate Polynomial Approximation and Point Reduction Procedure

被引：0
作者：
Nadezda Sukhorukova
Julien Ugon
David Yost
机构：
[1] Swinburne University of Technology,Centre for Informatics and Applied Optimization
[2] Deakin University,undefined
[3] Federation University Australia,undefined
来源：
Constructive Approximation | 2021年 / 53卷
关键词：
Multivariate polynomials; Chebyshev approximation; Best approximation conditions; 49J52; 90C26; 41A15; 41A50;
D O I：
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摘要：
We apply the methods of nonsmooth and convex analysis to extend the study of Chebyshev (uniform) approximation for univariate polynomial functions to the case of general multivariate functions (not just polynomials). First of all, we give new necessary and sufficient optimality conditions for multivariate approximation, and a geometrical interpretation of them which reduces to the classical alternating sequence condition in the univariate case. Then, we present a procedure for verification of necessary and sufficient optimality conditions that is based on our generalization of the notion of alternating sequence to the case of multivariate polynomials. Finally, we develop an algorithm for fast verification of necessary optimality conditions in the multivariate polynomial case.
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页码：529 / 544
页数：15
相关论文
共 11 条
  • [1] Davydov OV(1998)Approximation order of bivariate spline interpolation for arbitrary smoothness J. Comput. Appl. Math. 90 117-134
  • [2] Nürnberger G(1911)Sur la méthode de l’approximation minimum Annales de la Société Scientifique de Bruxelles 35 1-16
  • [3] Zeilfelder F(2000)Interpolation by spline spaces on classes of triangulations J. Comput. Appl. Math. 119 347-376
  • [4] de la Vallée Poussin CJ(1957)General computational methods of Chebyshev approximation Atomic Energy Comm. Transl. 4491 1-85
  • [5] Nürnberger G(1963)Tchebycheff approximation in several variables Trans. Amer. Math. Soc. 109 444-466
  • [6] Zeilfelder F(1967)Characterization of Chebyshev approximation by splines SIAM J. Numer. Anal. 4 557-567
  • [7] Remez E(1968)Uniform approximation by Chebyshev spline functions. II: free knots SIAM J. Numer. Anal. 5 647-656
  • [8] Rice J(2010)Vallée–Poussin theorem and Remez algorithm in the case of generalised degree polynomial spline approximation Pac. J. Optim. 6 103-114
  • [9] Rice J(undefined)undefined undefined undefined undefined-undefined
  • [10] Schumaker L(undefined)undefined undefined undefined undefined-undefined
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