A new algorithm for the Chebyshev solution of overdetermined linear systems

Abstract

Let x ( p ) x(p) be the point which minimizes the residual of a linear system in the l p {l_p} norm. It is known that under certain conditions x ( p ) → x ∗ x(p) \to {x^\ast } , the Chebyshev or l ∞ {l_\infty } solution, as p → ∞ p \to \infty . A differential equation describing x ( p ) x(p) is derived from which an iterative scheme is devised. A convergence analysis is given and numerical results are presented.