Remote Access Mathematics of Computation
Green Open Access

Mathematics of Computation

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

Request Permissions   Purchase Content 
 

 

A variant of the AOR method for augmented systems


Authors: M. M. Martins, W. Yousif and J. L. Santos
Journal: Math. Comp. 81 (2012), 399-417
MSC (2010): Primary 65F10
DOI: https://doi.org/10.1090/S0025-5718-2011-02483-X
Published electronically: June 16, 2011
MathSciNet review: 2833501
Full-text PDF

Abstract | References | Similar Articles | Additional Information

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).


References [Enhancements On Off] (What's this?)


Similar Articles

Retrieve articles in Mathematics of Computation with MSC (2010): 65F10

Retrieve articles in all journals with MSC (2010): 65F10


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

DOI: https://doi.org/10.1090/S0025-5718-2011-02483-X
Keywords: AOR-like method, SOR-like method, MAOR-like method, MSOR-like method, SSOR-like method, saddle point problem, augmented system, iterative methods
Received by editor(s): August 7, 2009
Received by editor(s) in revised form: September 20, 2010
Published electronically: June 16, 2011
Article copyright: © Copyright 2011 American Mathematical Society