Applied Mathematics and Computation, ( ISI ), Volume (176), No (2), Year (2006-5) , Pages (727-738)

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 ,

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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.

Keywords

Iterative methods; Significant digits; FOM algorithm; Error propagation; Stochastic arithmetic; CADNA
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@article{paperid:202381,
author = { -, - and Toutounian Mashhad, Faezeh},
title = {Numerical accuracy of a certain class of iterative methods for solving linear system},
journal = {Applied Mathematics and Computation},
year = {2006},
volume = {176},
number = {2},
month = {May},
issn = {0096-3003},
pages = {727--738},
numpages = {11},
keywords = {Iterative methods; Significant digits; FOM algorithm; Error propagation; Stochastic arithmetic; CADNA library},
}

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%0 Journal Article
%T Numerical accuracy of a certain class of iterative methods for solving linear system
%A -, -
%A Toutounian Mashhad, Faezeh
%J Applied Mathematics and Computation
%@ 0096-3003
%D 2006

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