Factorised Preconditionings of Successive Approximations in Finite Precision

This paper examines the possibility of using the method of successive approximations for the approximate solution of a large system of linear equations with a dense, noncontraction, and ill-conditioned matrix. Using Krasnosel'skii's method of transformation of linear operator equations and functional calculi, the procedure of factorised preconditionings of successive approximations is developed and analysed in the finite precision arithmetic. Numerical results of computational experiments are presented to demonstrate the practicability of the proposed approach.This revised version was published online in October 2005 with corrections to the Cover Date.