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AIMS Mathematics

2021, Volume 6, Issue 4: 4105-4118. doi: 10.3934/math.2021243
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Research article

Shift-splitting iteration methods for a class of large sparse linear matrix equations

  • Department of Applied Mathematics, School of Science, Lanzhou University of Technology, Lanzhou 730050, P. R. China
  • Received: 01 December 2020 Accepted: 01 February 2021 Published: 05 February 2021

  • MSC : 15A24, 15A30, 15A69, 65F10, 65F30, 65F50, 65H10

  • By utilizing an inner-outer iteration strategy, a shift-splitting (SS) iteration method to solve a class of large sparse linear matrix equation $ AXB = C $ is proposed in this work. Two convergence theorems for differential forms are studied in depth. Moreover, the quasi-optimal parameters which minimize the upper bound for the spectral radius of SS iteration matrix are given. Two numerical examples illustrate the high-efficiency of SS iteration method, especially when coefficient matrices are ill-conditioned.

    Citation: Xu Li, Rui-Feng Li. Shift-splitting iteration methods for a class of large sparse linear matrix equations[J]. AIMS Mathematics, 2021, 6(4): 4105-4118. doi: 10.3934/math.2021243

    Related Papers:

  • By utilizing an inner-outer iteration strategy, a shift-splitting (SS) iteration method to solve a class of large sparse linear matrix equation $ AXB = C $ is proposed in this work. Two convergence theorems for differential forms are studied in depth. Moreover, the quasi-optimal parameters which minimize the upper bound for the spectral radius of SS iteration matrix are given. Two numerical examples illustrate the high-efficiency of SS iteration method, especially when coefficient matrices are ill-conditioned.


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