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Chebyshev approximation by A+B*ϕ(CX)

Chebyshev Approximation durch A+B*ϕ(CX)

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Abstract

A sufficient condition is given for best Chebyshev approximations of the form a+bϕ(cx) to be characterized by alternation of their error curve. Several examples are given of ϕ for which alternation occurs. The problem of computing a best approximation is considered. It is shown for some ϕ that adding all first degree polynomials to the family of approximations still gives an alternating theory.

Zusammenfassung

Eine hinreichende Bedingung für beste Chebyshev Approximationen der Forma+bϕ(cx) wird angegeben und durch Alternanten ihrer Fehlerkurve charakterisiert. Gegeben werden mehrere Beispiele für ϕ in denen Alternanten vorkommen. Betrachtet wird das Problem, die beste Annäherung zu berechnen. Für einige Funktionen ϕ wird gezeigt, daß das Hinzufügen aller Polynome ersten Grades zu der Familie der Approximationen noch eine Alternantentheorie gibt.

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Authors and Affiliations

  1. Computer Science Department, University of Western Ontario, London 72, Canada

    Ch. B. Dunham

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  1. Ch. B. Dunham
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Dunham, C.B. Chebyshev approximation by A+B*ϕ(CX). Computing 13, 205–213 (1974). https://doi.org/10.1007/BF02241713

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  • DOI: https://doi.org/10.1007/BF02241713

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