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Efficient variants of the CMRH method for solving a sequence of multi-shifted non-Hermitian linear systems simultaneously

Gu, X-M., Huang, T-Z., Carpentieri, B., Imakura, A., Zhang, K. & Du, L., Sep-2020, In : Journal of Computational and Applied Mathematics. 375, 16 p., 112788.

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  • EfficientvariantsoftheCMRHmethodforsolving a sequence of multi-shiftednon-Hermitian linear systems simultaneously

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DOI

  • Xian-Ming Gu
  • Ting-Zhu Huang
  • Bruno Carpentieri
  • Akira Imakura
  • Ke Zhang
  • Lei Du

Multi-shifted linear systems with non-Hermitian coefficient matrices arise in numerical solutions of time-dependent partial/fractional differential equations (PDEs/FDEs), in control theory, PageRank problems, and other research fields. We derive efficient variants of the restarted Changing Minimal Residual method based on the cost-effective Hessenberg procedure (CMRH) for this problem class. Then, we introduce a flexible variant of the algorithm that allows to use variable preconditioning at each iteration to further accelerate the convergence of shifted CMRH. We analyse the performance of the new class of methods in the numerical solution of PDEs and FDEs, also against other multi-shifted Krylov subspace methods. (C) 2020 Elsevier B.V. All rights reserved.

Original languageEnglish
Article number112788
Number of pages16
JournalJournal of Computational and Applied Mathematics
Volume375
Publication statusPublished - Sep-2020

    Keywords

  • Krylov subspace methods, Shifted linear systems, Hessenberg procedure, GMRES, Shifted CMRH methods, FDEs, FULL ORTHOGONALIZATION METHOD, RESTARTED GMRES, KRYLOV METHODS, Q-OR, ALGORITHM, IMPLEMENTATION, CONVERGENCE, FAMILIES, BICG

ID: 127127935