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