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A unified framework for the construction of various matrix multisplitting iterative methods for large sparse system of linear equations |
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| Authors: | Zhong-Zhi Bai Jia-Chang Sun De-Ren Wang |
| Affiliation: | State Key Laboratory of Scientific/Engineering Computing Institute of Computational Mathematics and Scientific/Engineering Computing Chinese Academy of Sciences, P.O. Box 2719, Beijing 100080, P.R. China Institute of Software, Chinese Academy of Sciences P.O. Box 2719, Beijing 100080, P.R. China Department of Mathematics, Shanghai University, Shanghai 201800, P.R. China |
| Abstract: | A unified framework for the construction of various synchronous and asynchronous parallel matrix multisplitting iterative methods, suitable to the SIMD and MIMD multiprocessor systems, respectively, is presented, and its convergence theory is established under rather weak conditions. These afford general method models and systematical convergence criterions for studying the parallel iterations in the sense of matrix multisplitting. In addition, how the known parallel matrix multisplitting iterative methods can be classified into this new framework, and what novel ones can be generated by it are shown in detail. |
| Keywords: | System of linear equations Parallel iteration Matrix multisplitting Relaxation method Convergence theory |
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