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Advances in Numerical Analysis
Volume 2013 (2013), Article ID 732032, 6 pages
http://dx.doi.org/10.1155/2013/732032
Research Article

Convergent Homotopy Analysis Method for Solving Linear Systems

School of Mathematical Sciences, Ferdowsi University of Mashhad, P.O. Box 1159-91775, Mashhad, Iran

Received 16 June 2013; Accepted 22 August 2013

Academic Editor: Ting-Zhu Huang

Copyright © 2013 H. Nasabzadeh and F. Toutounian. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Abstract

By using homotopy analysis method (HAM), we introduce an iterative method for solving linear systems. This method (HAM) can be used to accelerate the convergence of the basic iterative methods. We also show that by applying HAM to a divergent iterative scheme, it is possible to construct a convergent homotopy-series solution when the iteration matrix G of the iterative scheme has particular properties such as being symmetric, having real eigenvalues. Numerical experiments are given to show the efficiency of the new method.