Bounding the error of a continuous approximation for linear systems

Abstract

We present preconditioned interval Gauss-Siedel method and interval LU decomposition for finding solution to the interval linear system of equation Ad=b where the nxn coefficient matrix A lies between two bounds A and A and b„¡ƒËb,b ƒÍ. It is found out that preconditioned interval methods of Gauss-Siedel and LU have substantial reduction of excess widths of the interval hull of the solution set. In particular we also give our results in terms of midpoint-radius arithmetic for Gauss-Siedel method in the sense analogous to (Rump,1999) and (Gargantini and Henrici,1972) circular interval arithmetic.