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The Chebyshev Equioscillation Theorem

Author(s): 
Robert Mayans

Author Information

Robert Mayans is an Assistant Professor of Mathematics at Fairleigh Dickinson University

Abstract

The Chebyshev equioscillation theorem describes a striking pattern between a continuous function on a closed interval, and its best approximating polynomial of degree n. Although it is a result of great influence in the theory of polynomial approximation, the theorem is usually omitted from the undergraduate numerical analysis course because of its somewhat complicated proof. Our aim in this paper is to use applets to motivate and illustrate the theorem and its proof.

Technologies Used in This Article

This article uses Java for several interactive mathlets. Click on the link to install the Java plug-in if necessary. The article is given in two forms.

  • The HTML version uses PNG images for mathematical expressions.
  • The XML version uses MathML (the Mathematics Markup Language) for mathematical expressions.

The XML/MathML version is supported by the Mozilla Firefox browser (version 1.5 or later) with the MathML fonts installed, and on the Microsoft Windows platform by the Internet Explorer browser (version 6.0 or later) with the MathPlayer plug-in (version 2.0b or later). Click on the links to upgrade your browser. The MathML version has several advantages:

  • The mathematical expressions look better.
  • Expressions can be resized, and in general behave like the surrounding text.
  • In some cases expressions can be exported into other applications.

Publication Data

Published December, 2006. Article ID: 1316
Copyright © 2006 by Robert Mayans

Article Links

Robert Mayans, "The Chebyshev Equioscillation Theorem," Loci (February 2007)

JOMA

Journal of Online Mathematics and its Applications

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