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

  • Hiroto TadanoEmail author
Special Feature: Original Paper International Workshop on Eigenvalue Problems: Algorithms; Software and Applications, in Petascale Computing (EPASA2018)


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.


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

Mathematics Subject Classification

65F10 Iterative methods for linear systems 65F50 Sparse matrices 



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Copyright information

© The JJIAM Publishing Committee and Springer Japan KK, part of Springer Nature 2019

Authors and Affiliations

  1. 1.Center for Computational SciencesUniversity of TsukubaTsukubaJapan

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