On Minimization of Upper Bound for the Convergence Rate of the QHSS Iteration Method

doi:10.1007/s42967-019-00015-y

Communications on Applied Mathematics and Computation ›› 2019, Vol. 1 ›› Issue (2): 263-282.doi: 10.1007/s42967-019-00015-y

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On Minimization of Upper Bound for the Convergence Rate of the QHSS Iteration Method

Wen-Ting Wu^1,2

1 State Key Laboratory of Scientifc/Engineering Computing, Institute of Computational Mathematics and Scientifc/Engineering Computing, Academy of Mathematics and Systems Science, Chinese Academy of Sciences, P. O. Box 2719, Beijing 100190, China;
2 School of Mathematical Sciences, University of Chinese Academy of Sciences, Beijing 100049, China

收稿日期:2018-04-18 修回日期:2018-07-20 出版日期:2019-06-20 发布日期:2019-06-20
通讯作者: Wen-Ting Wu E-mail:wuwenting@lsec.cc.ac.cn
基金资助:
The author is thankful to the referees for their constructive comments and valuable suggestions, which greatly improved the original manuscript of this paper. Supported by the National Natural Science Foundation (No. 11671393), China.

On Minimization of Upper Bound for the Convergence Rate of the QHSS Iteration Method

Wen-Ting Wu^1,2

1 State Key Laboratory of Scientifc/Engineering Computing, Institute of Computational Mathematics and Scientifc/Engineering Computing, Academy of Mathematics and Systems Science, Chinese Academy of Sciences, P. O. Box 2719, Beijing 100190, China;
2 School of Mathematical Sciences, University of Chinese Academy of Sciences, Beijing 100049, China

Received:2018-04-18 Revised:2018-07-20 Online:2019-06-20 Published:2019-06-20
Contact: Wen-Ting Wu E-mail:wuwenting@lsec.cc.ac.cn
Supported by:
The author is thankful to the referees for their constructive comments and valuable suggestions, which greatly improved the original manuscript of this paper. Supported by the National Natural Science Foundation (No. 11671393), China.

摘要/Abstract

摘要： For an upper bound of the spectral radius of the QHSS (quasi Hermitian and skew-Hermitian splitting) iteration matrix which can also bound the contraction factor of the QHSS iteration method, we give its minimum point under the conditions which guarantee that the upper bound is strictly less than one. This provides a good choice of the involved iteration parameters, so that the convergence rate of the QHSS iteration method can be signifcantly improved.

关键词: System of linear equations, Non-Hermitian matrix, QHSS iteration method, Convergence rate

Abstract: For an upper bound of the spectral radius of the QHSS (quasi Hermitian and skew-Hermitian splitting) iteration matrix which can also bound the contraction factor of the QHSS iteration method, we give its minimum point under the conditions which guarantee that the upper bound is strictly less than one. This provides a good choice of the involved iteration parameters, so that the convergence rate of the QHSS iteration method can be signifcantly improved.

Key words: System of linear equations, Non-Hermitian matrix, QHSS iteration method, Convergence rate

中图分类号:

Wen-Ting Wu. On Minimization of Upper Bound for the Convergence Rate of the QHSS Iteration Method[J]. Communications on Applied Mathematics and Computation, 2019, 1(2): 263-282.

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On Minimization of Upper Bound for the Convergence Rate of the QHSS Iteration Method

On Minimization of Upper Bound for the Convergence Rate of the QHSS Iteration Method

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