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Applications of stair matrices and their generalizations to iterative methods

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Abstract

Stair matrices and their generalizations are introduced. The definitions and some properties of the matrices were first given by Lu Hao. this class of matrices provide bases of matrix splittings for iterative methods. The remarkable feature of iterative methods based on the new class of matrices is that the methods are easily implemented for parallel computation. In particular, a generalization of the accelerated overrelaxation method (GAOR) is introduced. Some theories of the AOR method are extended to the generalized method to include a wide class of matrices. The convergence of the new method is derived for Hermitian positive definite matrices. Finally, some examples are given in order to show the superiority of the new method.

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Authors and Affiliations

  1. Department of Mathematics, Northeastern University, Shenyang, 110004, P. R. China

    Shao Xin-hui Doctor  (邵新慧), Shen Hai-long  (沈海龙) & Li Chang-jun  (李长军)

Authors
  1. Shao Xin-hui Doctor  (邵新慧)
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  2. Shen Hai-long  (沈海龙)
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  3. Li Chang-jun  (李长军)
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Corresponding author

Correspondence to Shao Xin-hui Doctor  (邵新慧).

Additional information

Communicated by GU Yuan-xian

Project supported by the Natural Science Foundation of Liaoning Province of China (No.20022021)

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Shao, Xh., Shen, Hl. & Li, Cj. Applications of stair matrices and their generalizations to iterative methods. Appl Math Mech 27, 1115–1121 (2006). https://doi.org/10.1007/s10483-006-0812-y

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  • DOI: https://doi.org/10.1007/s10483-006-0812-y

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Chinese Library Classification

2000 Mathematics Subject Classification

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