Rational functions with positive coefficients, polynomials and uniform approximations

Peter B. Borwein

Vol. 88 (1980), No. 1, 55–68

DOI: 10.2140/pjm.1980.88.55

Abstract

Upper bounds are established for the uniform approximation of continuous functions on [1, 0] by rational functions with positive coefficients. These bounds are obtained by rewriting polynomials with no positive roots as rational functions with positive coefficients.

Mathematical Subject Classification 2000

Primary: 41A29

Secondary: 41A20

Milestones

Received: 19 July 1978

Published: 1 May 1980