Scientific Research and Essays

  • Abbreviation: Sci. Res. Essays
  • Language: English
  • ISSN: 1992-2248
  • DOI: 10.5897/SRE
  • Start Year: 2006
  • Published Articles: 2752

Full Length Research Paper

A collection of new preconditioners for solving linear systems

H. Saberi Najafi1 and S. A. Edalatpanah1,2*
1Department of Applied Mathematics, Lahijan Branch, Islamic Azad University, Lahijan, Iran. 2Young Researchers Club, Lahijan Branch, Islamic Azad University, Lahijan, Iran.
Email: [email protected]

  •  Accepted: 07 January 2013
  •  Published: 18 August 2013

Abstract

In this paper, new preconditioners from class of (I+S)-type for solving linear systems are developed and preconditioned, accelerated overrelaxation (AOR) method is used for the systems. The proposed algorithms have a simple and graceful structure. Asymptotic convergence of the sequence generated by the methods to the unique solution of linear systems is proved, along with a result regarding the convergence rate of the preconditioned methods. Finally, computational comparisons of the standard methods against preconditioned methods based on examples are presented which illustrate the merits of simplicity, power and effectiveness of the proposed algorithms.

 

Key words: Preconditioning, accelerated overrelaxation (AOR), successive over relaxation (SOR), Z-, M- matrix.