Polynomial approximation using equioscillation on the extreme points of Chebyshev polynomials

Abstract

One method of obtaining near minimax polynomial approximation to f ∈ C(n + 1)[-1, 1] is to choose p ∈ Pn such that f - p equioscillates on the point set consisting of the extrema of Tn + 1. It is shown that ∥f - p∥ may be expressed in terms of f(n + 1) in the same manner as En(f), the error of minimax approximation. The Lebesgue constants are also investigated. © 1982.