The Approached Solutions of Ill-Conditioned SLAE with Inexact Factor

K. F. Ivanova, Associate Professor, e-mail: klara.i2010@yandex.ru, Saint-Petersburg State University

Estimations of a approached solutions of systems linear algebraic equations (SLAE) with ill-conditioned matrix and inexact coefficients and right-hand side are proposed. It is shown that estimation of solutions of the systems generated by "a sign" technique, are similar to the algebraic estimation for outer problem of the united set of solution interval systems linear algebraic equations (ISLAE) with interval matrixes. Association between occurrence of considerable errors of the solution linear systems by application of the "sign" technique initiating ill-conditioned matrixes, leading to an incorrect problem is considered. Regularization operators with numerical algorithm developed on the basis of A. N. Tikhonov's concept for a correct problems and construction of the approached steady solutions against small changes of the entrance data are used.

Keywords: linear algebraic equations, "sign" technique, interval system, regularization operators, incorrect problem, approached solution

pp. 40–48