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Volume 32, Issue 3
Parallel Quasi-Chebyshev Acceleration to Nonoverlapping Multisplitting Iterative Methods Based on Optimization

Ruiping Wen, Guoyan Meng & Chuanlong Wang

DOI: 10.4208/jcm.1401-CR1

J. Comp. Math., 32 (2014), pp. 284-296.

Published online: 2014-06

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  • Abstract

In this paper, we present a parallel quasi-Chebyshev acceleration applied to the nonoverlapping multisplitting iterative method for the linear systems when the coefficient matrix is either an $H$-matrix or a symmetric positive definite matrix. First, $m$ parallel iterations are implemented in $m$ different processors. Second, based on $l_1$-norm or $l_2$-norm, the $m$ optimization models are parallelly treated in $m$ different processors. The convergence theories are established for the parallel quasi-Chebyshev accelerated method. Finally, the numerical examples show that the parallel quasi-Chebyshev technique can significantly accelerate the nonoverlapping multisplitting iterative method.

  • Keywords

Parallel quasi-Chebyshev acceleration, Nonoverlapping multisplitting iterative method, Convergence, Optimization.

  • AMS Subject Headings

65F10, 65F50, 15A06.

  • Copyright

COPYRIGHT: © Global Science Press

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@Article{JCM-32-284, author = {Ruiping Wen, Guoyan Meng and Chuanlong Wang}, title = {Parallel Quasi-Chebyshev Acceleration to Nonoverlapping Multisplitting Iterative Methods Based on Optimization}, journal = {Journal of Computational Mathematics}, year = {2014}, volume = {32}, number = {3}, pages = {284--296}, abstract = {

In this paper, we present a parallel quasi-Chebyshev acceleration applied to the nonoverlapping multisplitting iterative method for the linear systems when the coefficient matrix is either an $H$-matrix or a symmetric positive definite matrix. First, $m$ parallel iterations are implemented in $m$ different processors. Second, based on $l_1$-norm or $l_2$-norm, the $m$ optimization models are parallelly treated in $m$ different processors. The convergence theories are established for the parallel quasi-Chebyshev accelerated method. Finally, the numerical examples show that the parallel quasi-Chebyshev technique can significantly accelerate the nonoverlapping multisplitting iterative method.

}, issn = {1991-7139}, doi = {https://doi.org/10.4208/jcm.1401-CR1}, url = {http://global-sci.org/intro/article_detail/jcm/9886.html} }
TY - JOUR T1 - Parallel Quasi-Chebyshev Acceleration to Nonoverlapping Multisplitting Iterative Methods Based on Optimization AU - Ruiping Wen, Guoyan Meng & Chuanlong Wang JO - Journal of Computational Mathematics VL - 3 SP - 284 EP - 296 PY - 2014 DA - 2014/06 SN - 32 DO - http://doi.org/10.4208/jcm.1401-CR1 UR - https://global-sci.org/intro/article_detail/jcm/9886.html KW - Parallel quasi-Chebyshev acceleration, Nonoverlapping multisplitting iterative method, Convergence, Optimization. AB -

In this paper, we present a parallel quasi-Chebyshev acceleration applied to the nonoverlapping multisplitting iterative method for the linear systems when the coefficient matrix is either an $H$-matrix or a symmetric positive definite matrix. First, $m$ parallel iterations are implemented in $m$ different processors. Second, based on $l_1$-norm or $l_2$-norm, the $m$ optimization models are parallelly treated in $m$ different processors. The convergence theories are established for the parallel quasi-Chebyshev accelerated method. Finally, the numerical examples show that the parallel quasi-Chebyshev technique can significantly accelerate the nonoverlapping multisplitting iterative method.

Ruiping Wen, Guoyan Meng and Chuanlong Wang. (2014). Parallel Quasi-Chebyshev Acceleration to Nonoverlapping Multisplitting Iterative Methods Based on Optimization. Journal of Computational Mathematics. 32 (3). 284-296. doi:10.4208/jcm.1401-CR1
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