The remez algorithm for biased uniform approximation on an interval

Abstract

Uniform approximation on an interval [α β] by an alternating family when positive deviations (errors) are magnified by a bias factor is considered. This problem is related to one-sided uniform approximation from above for large bias factors. Best approximations are characterized by alternation, suggesting use of the first author's variant of the Remez 2nd algorithm for generalized weight functions. Previously written subprograms of the authors are combined with minor modifications to produce a general subprogram for families satisfying the hypotheses of Meinardus and Schwedt.

Keywords:

• Remez algorithm
• biased minimax approximation
• alternation
• interval
• nonlinear