An algorithm for best generalised rational approximation of continuous functions

The motivation of this paper is the development of an optimisation method for solving optimisation problems appearing in Chebyshev rational and generalised rational approximation problems, where the approximations are constructed as ratios of linear forms (linear combinations of basis functions). Th...

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Main Authors Millán, R. Díaz, Sukhorukova, Nadezda, Ugon, Julien
Format Journal Article
LanguageEnglish
Published 05.11.2020
Subjects
Computer Science - Numerical Analysis
Mathematics - Numerical Analysis
Mathematics - Optimization and Control
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DOI10.48550/arxiv.2011.02721

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Summary:The motivation of this paper is the development of an optimisation method for solving optimisation problems appearing in Chebyshev rational and generalised rational approximation problems, where the approximations are constructed as ratios of linear forms (linear combinations of basis functions). The coefficients of the linear forms are subject to optimisation and the basis functions are continuous function. It is known that the objective functions in generalised rational approximation problems are quasi-convex. In this paper we also prove a stronger result, the objective functions are pseudo-convex in the sense of Penot and Quang. Then we develop numerical methods, that are efficient for a wide range of pseudo-convex functions and test them on generalised rational approximation problems.
DOI:10.48550/arxiv.2011.02721