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A block GMRES method with deflated restarting for solving linear systems with multiple shifts and multiple right‐hand sides
Author(s) -
Sun DongLin,
Huang TingZhu,
Jing YanFei,
Carpentieri Bruno
Publication year - 2018
Publication title -
numerical linear algebra with applications
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.02
H-Index - 53
eISSN - 1099-1506
pISSN - 1070-5325
DOI - 10.1002/nla.2148
Subject(s) - generalized minimal residual method , krylov subspace , mathematics , preconditioner , linear system , block (permutation group theory) , sequence (biology) , eigenvalues and eigenvectors , residual , algorithm , convergence (economics) , iterative method , mathematical optimization , combinatorics , mathematical analysis , quantum mechanics , physics , biology , economics , genetics , economic growth
Summary The restarted block generalized minimum residual method (BGMRES) with deflated restarting (BGMRES‐DR) was proposed by Morgan to dump the negative effect of small eigenvalues from the convergence of the BGMRES method. More recently, Wu et al. introduced the shifted BGMRES method (BGMRES‐Sh) for solving the sequence of linear systems with multiple shifts and multiple right‐hand sides. In this paper, a new shifted block Krylov subspace algorithm that combines the characteristics of both the BGMRES‐DR and the BGMRES‐Sh methods is proposed. Moreover, our method is enhanced with a seed selection strategy to handle the case of almost linear dependence of the right‐hand sides. Numerical experiments illustrate the potential of the proposed method to solve efficiently the sequence of linear systems with multiple shifts and multiple right‐hand sides, with and without preconditioner, also against other state‐of‐the‐art solvers.