Title : Numerical accuracy of a certain class of iterative methods for solving linear system ( Numerical accuracy of a certain class of iterative methods for solving linear system )
Authors: - - , Faezeh Toutounian Mashhad ,Access to full-text not allowed by authors
Abstract
One of the most important problem for solving the linear system Ax = b, by using the iterative methods, is to use a good stopping criterion and to determine the common significant digits between each corresponding components of computed solution and exact solution. In this paper, for a certain class of iterative methods, we propose a way to determine the number of common significant digits of xm and x, where xm and x are computed solution at iteration m and exact solution, respectively. By using the CADNA library which allows us to estimate the round-off error effect on any computed result, we also propose a good stopping criterion which is able to stop the process as soon as a satisfactory informatical solution is obtained. Numerical examples are used to show the good numerical properties.