Error bounds for a near-minimax approximation

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.