An Implementation of the Remez Algorithm as an Eigenvalue Problem
by
Allan W. McInnes
University of Canterbury

The characterization of the best uniform approximation to a continuous function from a finite dimensional linear subspace is given by the Chebyshev Equioscillation Theorem. However there are very few functions for which the best appproximation can be found explicitly, and in general we must resort to a computational algorithm to obtain an approximate solution. One such popular algorithm, which uses the characterization theorem, is the exchange algorithm of Remez, and the usual implementation is as a single (point) exchange.

A more general version of the Remez algorithm is the multiple (point) exchange. This version of the algorithm is of interest because it lends itself more naturally to generalizations, particularly if it is interpreted as an eigenvalue problem. This paper is an introduction to the implementation of the Remez algorithm as an eigenvalue problem and discusses the resolution of some of the problems that may arise.

Date received: June 28, 1998