Rate of convergence of the linear discrete Polya algorithm

In this paper we consider the problem of best approximation in l(p), 1 < p <less than or equal to> infinity. If h(p), 1 < p < infinity, denotes the be st p-approximation of the element h is an element of R-n from a proper affi ne subspace K of R-n, h is not an element of K, then lim(p-->infinity) h(p) =h(infinity)*, where h(infinity)* is a best uniform approximation of h fro m K, the so-called strict uniform approximation. Our aim is to give a compl ete description of the rate of convergence of parallel toh(p) - h(infinity) *parallel to as p --> infinity. (C) 2001 Academic Press.