Rate of convergence of the linear discrete pólya 1-algorithm

Abstract

In this paper, we consider the problem of best approximation in ℓp (n), 1 ≤p ≤ ∞. If hp, 1 ≤ p ≤ ∞, denotes the best ℓp-approximation of the element h ∈ ℝn from a proper affine subspace K of ℝn, h ∉ K, then limp→1 hp = h1*, where h1* is a best ℓ1-approximation of h from K, the so-called natural ℓ1-approximation. Our aim is to give a complete description of the rate of convergence to hp to h1* as p → 1. © 20002 Elsevier Science (USA).