An algorithm for best generalised rational approximation of continuous functions

2020/11/05 by R. Díaz Millán, Millán, R. Díaz, Nadezda Sukhorukova +3
Computer Science · Mathematics · #65D15 #90C25 #90C26 #90C47 #90C90 #Advanced Optimization Algorithms Research #FOS: Mathematics #Numerical Analysis (math.NA) #Optimization and Control (math.OC) #Optimization and Variational Analysis

paper · pdf · doi:10.48550/arxiv.2011.02721

openalex publication_date 2020/11/05 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

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.

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