Parallel Quasi-Chebyshev Acceleration to Nonoverlapping Multisplitting Iterative Methods Based on Optimization
Year: 2014
Journal of Computational Mathematics, Vol. 32 (2014), Iss. 3 : pp. 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.
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Journal Article Details
Publisher Name: Global Science Press
Language: English
DOI: https://doi.org/10.4208/jcm.1401-CR1
Journal of Computational Mathematics, Vol. 32 (2014), Iss. 3 : pp. 284–296
Published online: 2014-01
AMS Subject Headings:
Copyright: COPYRIGHT: © Global Science Press
Pages: 13
Keywords: Parallel quasi-Chebyshev acceleration Nonoverlapping multisplitting iterative method Convergence Optimization.
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Modified quasi-Chebyshev acceleration to nonoverlapping parallel multisplitting method
Wen, Rui-Ping
Ren, Fu-Jiao
Meng, Guo-Yan
Numerical Algorithms, Vol. 75 (2017), Iss. 4 P.1123
https://doi.org/10.1007/s11075-016-0234-4 [Citations: 0]