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2022, Volume 7, Issue 5: 7625-7641. doi: 10.3934/math.2022428
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Research article

Generalized accelerated AOR splitting iterative method for generalized saddle point problems

  • Computer Information Engineering College, Guizhou University of Commerce, Guiyang 550014, China
  • Received: 03 August 2021 Revised: 29 January 2022 Accepted: 08 February 2022 Published: 15 February 2022

  • MSC : 65F10, 65F50

  • Generalized accelerated AOR (GAAOR) splitting iterative method for the generalized saddle point problems is proposed in this paper. The iterative scheme and the convergence of the GAAOR splitting method are researched. The eigenvalues distributions of its preconditioned matrix is discussed under {two different choices of the parameter matrix Q}. The resulting GAAOR preconditioner is used to precondition Krylov subspace method such as the restarted generalized minimal residual (GMRES) method for solving the equivalent formulation of the generalized saddle point problems. The theoretical results and effectiveness of the GAAOR splitting iterative method are supported by {some} numerical examples.

    Citation: Jin-Song Xiong. Generalized accelerated AOR splitting iterative method for generalized saddle point problems[J]. AIMS Mathematics, 2022, 7(5): 7625-7641. doi: 10.3934/math.2022428

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  • Generalized accelerated AOR (GAAOR) splitting iterative method for the generalized saddle point problems is proposed in this paper. The iterative scheme and the convergence of the GAAOR splitting method are researched. The eigenvalues distributions of its preconditioned matrix is discussed under {two different choices of the parameter matrix Q}. The resulting GAAOR preconditioner is used to precondition Krylov subspace method such as the restarted generalized minimal residual (GMRES) method for solving the equivalent formulation of the generalized saddle point problems. The theoretical results and effectiveness of the GAAOR splitting iterative method are supported by {some} numerical examples.


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