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Mathematics of Computation

Published by the American Mathematical Society, the Mathematics of Computation (MCOM) is devoted to research articles of the highest quality in all areas of pure and applied mathematics.

ISSN 1088-6842 (online) ISSN 0025-5718 (print)

The 2020 MCQ for Mathematics of Computation is 1.98.

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A variant of the AOR method for augmented systems
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by M. M. Martins, W. Yousif and J. L. Santos PDF
Math. Comp. 81 (2012), 399-417 Request permission

Abstract:

In this paper we present a variant of the Accelerated Overrelaxation iterative method (AOR), denoted by modified AOR-like method (MAOR-like method) for solving the augmented systems, i.e., the AOR-like method with three real parameters $\omega$, $r$ and $\alpha$. For special values of $\omega$, $r$ and $\alpha$ we get the MSOR-like method, the AOR-like method and the SOR-like method. An equation relating the involved parameters and the eigenvalues of the iteration matrix of the MAOR-like method is obtained. Furthermore, some convergence conditions for the MAOR-like method are derived. This paper generalizes the main results of Li, Li, Nie, and Evans 2004 and Shao, Li, and Li (2007). Numerical examples are presented to show that, for a suitable choice of the involved parameters, the MAOR-like method is superior when compared to the above iterative methods and to the SSOR-like method presented by Zheng, Wang, and Wu (2009).
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Additional Information
  • M. M. Martins
  • Affiliation: Department of Mathematics, University of Coimbra, Apartado 3008, EC Universidade, 3001-454 Coimbra, Portugal
  • Address at time of publication: Institute of Telecommunications, University of Coimbra, 3000 Coimbra, Portugal
  • Email: mmartins@mat.uc.pt
  • W. Yousif
  • Affiliation: Department of Computer Science, Loughborough University, Loughborough, LE11 3TU, Leicestershire, United Kingdom
  • Email: W.Yousif@lboro.ac.uk
  • J. L. Santos
  • Affiliation: Department of Mathematics, University of Coimbra, Apartado 3008, EC Universidade, 3001-454 Coimbra, Portugal
  • Address at time of publication: CMUC, Department of Mathematics, University of Coimbra, 3001-454 Coimbra, Portugal
  • Email: zeluis@mat.uc.pt
  • Received by editor(s): August 7, 2009
  • Received by editor(s) in revised form: September 20, 2010
  • Published electronically: June 16, 2011
  • © Copyright 2011 American Mathematical Society
  • Journal: Math. Comp. 81 (2012), 399-417
  • MSC (2010): Primary 65F10
  • DOI: https://doi.org/10.1090/S0025-5718-2011-02483-X
  • MathSciNet review: 2833501