Abstract
For solving an augmented linear system, Njeru and Guo presented an accelerated SOR-like (ASOR) method in (P. N. Njeru and X.-P. Guo. Accelerated SOR-like method for augmented linear systems, BIT Numerical Mathematics. 56, 557–571 2016). By further accelerating the ASOR method, we introduce another parameter and propose a modified ASOR method. We first characterize properties about eigenpairs of the iteration matrix, then discuss the convergence of the modified ASOR method. Numerical experiments are given to show the effectiveness of the modified ASOR method.
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Acknowledgments
We would like to express our sincere thanks to Prof. Tetsuya Sakurai and the two referees for their insightful comments and invaluable suggestions that greatly improved the representation of this paper. The first author also would like to thanks Prof. Eric King-wah Chu for his helpful discussion.
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The second is supported in part by National Natural Science Foundation of China under grants 11371145 and 11471122, and by the Science and Technology Commission of Shanghai Municipality under grant 13dz2260400.
The first and third authors are supported by National Natural Science Foundation of China under grant 11471122.
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Feng, TT., Guo, XP. & Chen, GL. A modified ASOR-like method for augmented linear systems. Numer Algor 82, 1097–1115 (2019). https://doi.org/10.1007/s11075-018-0644-6
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DOI: https://doi.org/10.1007/s11075-018-0644-6