A descent algorithm for linear continuous Chebyshev approximation

Abstract

This paper presents a direct, parameter-space descent algorithm for the linear continuous Chebyshev approximation problem. After suitable definition and characterization of edges and vertices, the search proceeds on a vertex-to-vertex basis. The advantage of the procedure is its generality, since the approximating set need not be a Chebyshev set, and a somewhat quicker time-to-convergence, at least on the examples attempted, than comparison algorithms. For approximation with non-Chebyshev sets the algorithm is defined up to a stop rule.