Geodesic
A deflated block flexible GMRES-DR method for linear systems with multiple right-hand sides
Electronic transactions on numerical analysis, Tome 41 (2014), pp. 478-496.

Voir la notice de l'article provenant de la source Electronic Library of Mathematics

Summary: This study is mainly focused on the iterative solution of multiple linear systems with several right-hand sides. To solve such systems efficiently, we first present a flexible version of block GMRES with deflation of eigenvalues according to [R. B. Morgan, Restarted block-GMRES with deflation of eigenvalues, Appl. Numer. Math., 54 (2005), pp. 222 -- 236] and then apply a modified block Arnoldi vector deflation technique to accelerate the convergence of this new flexible version. Incorporating this deflation technique, the new algorithm can address the possible linear dependence at each iteration during the block Arnoldi procedure and reduce computational expense. Moreover, by analyzing its main mathematical properties, we show that the vector deflation procedure arises from the non-increasing behavior of the singular values of the block residual. In addition, the new approach also inherits the property of deflating small eigenvalues to mitigate convergence slowdown. Finally, the effectiveness of the proposed method is illustrated by some numerical experiments.
Classification : 65F10, 65F50
Keywords: deflated BFGMRES-DR, block Krylov subspace, modified block arnoldi vector deflation, harmonic Ritz vectors, deflated block flexible arnoldi procedure, multiple right-hand sides 
@article{ETNA_2014__41__a1,
     author = {Meng, Jing and Zhu, Pei-Yong and Li, Hou-Biao and Gu, Xian-Ming},
     title = {A deflated block flexible {GMRES-DR} method for linear systems with multiple right-hand sides},
     journal = {Electronic transactions on numerical analysis},
     pages = {478--496},
     publisher = {mathdoc},
     volume = {41},
     year = {2014},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/ETNA_2014__41__a1/}
}
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Meng, Jing; Zhu, Pei-Yong; Li, Hou-Biao; Gu, Xian-Ming. A deflated block flexible GMRES-DR method for linear systems with multiple right-hand sides. Electronic transactions on numerical analysis, Tome 41 (2014), pp. 478-496. http://geodesic.mathdoc.fr/item/ETNA_2014__41__a1/