Rate of Convergence of the Linear Discrete Pólya 1-Algorithm

AbstractIn 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→1hp=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 of hp to h1* as p→1