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Volume 16, Issue 3
A Class of Asynchronous Matrix Multi-Splitting Multi-Parameter Relaxation Iterations

Zhongzhi Bai, Deren Wang & D.J. Evans

J. Comp. Math., 16 (1998), pp. 221-238.

Published online: 1998-06

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  • Abstract

A class of asynchronous matrix multi-splitting multi-parameter relaxation methods, including the asynchronous matrix multisplitting SAOR, SSOR and SGS methods as well as the known asynchronous matrix multisplitting AOR, SOR and GS methods, etc., is proposed for solving the large sparse systems of linear equations by making use of the principle of sufficiently using the delayed information. These new methods can greatly execute the parallel computational efficiency of the MIMD-systems, and are shown to be convergent when the coefficient matrices are $H$-matrices. Moreover, necessary and sufficient conditions ensuring the convergence of these methods are concluded for the case that the coefficient matrices are $L$-matrices.

  • Keywords

System of linear equations, asynchronous iteration, matrix multisplitting, relaxation, convergence.

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  • Copyright

COPYRIGHT: © Global Science Press

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@Article{JCM-16-221, author = {Bai , ZhongzhiWang , Deren and Evans , D.J.}, title = {A Class of Asynchronous Matrix Multi-Splitting Multi-Parameter Relaxation Iterations}, journal = {Journal of Computational Mathematics}, year = {1998}, volume = {16}, number = {3}, pages = {221--238}, abstract = {

A class of asynchronous matrix multi-splitting multi-parameter relaxation methods, including the asynchronous matrix multisplitting SAOR, SSOR and SGS methods as well as the known asynchronous matrix multisplitting AOR, SOR and GS methods, etc., is proposed for solving the large sparse systems of linear equations by making use of the principle of sufficiently using the delayed information. These new methods can greatly execute the parallel computational efficiency of the MIMD-systems, and are shown to be convergent when the coefficient matrices are $H$-matrices. Moreover, necessary and sufficient conditions ensuring the convergence of these methods are concluded for the case that the coefficient matrices are $L$-matrices.

}, issn = {1991-7139}, doi = {https://doi.org/}, url = {http://global-sci.org/intro/article_detail/jcm/9155.html} }
TY - JOUR T1 - A Class of Asynchronous Matrix Multi-Splitting Multi-Parameter Relaxation Iterations AU - Bai , Zhongzhi AU - Wang , Deren AU - Evans , D.J. JO - Journal of Computational Mathematics VL - 3 SP - 221 EP - 238 PY - 1998 DA - 1998/06 SN - 16 DO - http://doi.org/ UR - https://global-sci.org/intro/article_detail/jcm/9155.html KW - System of linear equations, asynchronous iteration, matrix multisplitting, relaxation, convergence. AB -

A class of asynchronous matrix multi-splitting multi-parameter relaxation methods, including the asynchronous matrix multisplitting SAOR, SSOR and SGS methods as well as the known asynchronous matrix multisplitting AOR, SOR and GS methods, etc., is proposed for solving the large sparse systems of linear equations by making use of the principle of sufficiently using the delayed information. These new methods can greatly execute the parallel computational efficiency of the MIMD-systems, and are shown to be convergent when the coefficient matrices are $H$-matrices. Moreover, necessary and sufficient conditions ensuring the convergence of these methods are concluded for the case that the coefficient matrices are $L$-matrices.

Bai , ZhongzhiWang , Deren and Evans , D.J.. (1998). A Class of Asynchronous Matrix Multi-Splitting Multi-Parameter Relaxation Iterations. Journal of Computational Mathematics. 16 (3). 221-238. doi:
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