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

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  • 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 date: 2018-04-18

  Revised date: 2018-07-20

  Online published: 2019-06-20

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.

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.

Cite this article

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 . DOI: 10.1007/s42967-019-00015-y

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