Convergent Homotopy Analysis Method for Solving Linear Systems. (8th October 2013)

• Record Type: Journal Article
• Authors: Nasabzadeh, H.; Toutounian, F.
• Other Names: Huang Ting-Zhu Academic Editor.
• Is Part Of: Advances in numerical analysis. Volume 2013(2013)
• Publication Date: 2013-10-08
• Subjects: Numerical analysis -- Periodicals; Numerical analysis; Periodicals; Electronic journals; 518
• DOI: 10.1155/2013/732032
• Languages: English
• ISSNs: 1687-9562

Abstract

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.