Development of the Block BiCGGR2 method for linear systems with multiple right-hand sides

Japan Journal of Industrial and Applied Mathematics volume 36, pages563–577(2019)Cite this article

Abstract

Block Krylov subspace methods are efficient iterative methods for solving linearsystems with multiple right-hand sides. The Block BiCGGR method is one of the Block Krylov subspace methods, and can generate highly accurate approximatesolutions. However, when the number of right-hand sides is large, this method becomes numerically unstable. In this paper, the Block BiCGGR2 method is proposed. This method is a numerically stable and highly accurate method than the Block BiCGGR method and the Block BiCGSTAB method. Numerical results illustrate the robustness and the accuracy of the approximate solutions of the Block BiCGGR2 method.

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  1. Center for Computational Sciences, University of Tsukuba, 1-1-1 Tennodai, Tsukuba, Ibaraki, 305-8577, Japan

    Hiroto Tadano

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  1. Hiroto Tadano
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Tadano, H. Development of the Block BiCGGR2 method for linear systems with multiple right-hand sides. Japan J. Indust. Appl. Math. 36, 563–577 (2019). https://doi.org/10.1007/s13160-019-00354-6

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Keywords

  • Block Krylov subspace methods
  • Linear systems with multiple right-hand sides

Mathematics Subject Classification

  • 65F10 Iterative methods for linear systems
  • 65F50 Sparse matrices