- Title
- Chebyshev multivariate polynomial approximation : alternance interpretation
- Creator
- Sukhorukova, Nadezda; Ugon, Julien; Yost, David
- Date
- 2018
- Type
- Text; Book chapter
- Identifier
- http://researchonline.federation.edu.au/vital/access/HandleResolver/1959.17/182618
- Identifier
- vital:16191
- Identifier
-
https://doi.org/10.1007/978-3-319-72299-3_8
- Identifier
- ISBN:2523-3041, 978-3-319-72299-3
- Abstract
- In this paper, we derive optimality conditions for Chebyshev approximation of multivariate functions. The theory of Chebyshev (uniform) approximation for univariate functions was developed in the late nineteenth and twentieth century. The optimality conditions are based on the notion of alternance (maximal deviation points with alternating deviation signs). It is not clear, however, how to extend the notion of alternance to the case of multivariate functions. There have been several attempts to extend the theory of Chebyshev approximation to the case of multivariate functions. We propose an alternative approach, which is based on the notion of convexity and nonsmooth analysis.
- Publisher
- Springer International Publishing
- Relation
- 2016 Matrix Annals p. 177-182
- Rights
- All metadata describing materials held in, or linked to, the repository is freely available under a CC0 licence
- Rights
- Copyright © Springer International Publishing AG, part of Springer Nature 2018
- Rights
- Open Access
- Full Text
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