Error bounds for a near-minimax approximation

Abstract

It is known that a near minimax polynomial approximation tof ∈C [−1, 1] is provided by a finite carrier projectionM n fromC[−1, 1] onto the subspace of all polynomials of degree ≤n, such thatM nf is a weighted least squares approximation off on the set consisting of the extreme points of the Chebyshev polynomialT 2n + 1. In this paper, upper bounds for the error ∥f−M n f∥∞ are given in terms of divided differences.