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Volume 25, Issue 5
A Flexible Preconditioned Arnoldi Method for Shifted Linear Systems

G.-D. Gu, X.-L. Zhou & Lei Lin

J. Comp. Math., 25 (2007), pp. 522-530.

Published online: 2007-10

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  • Abstract

We are interested in the numerical solution of the large nonsymmetric shifted linear system, $(A + \alpha I) x = b$, for many different values of the shift $\alpha$ in a wide range. We apply the Saad's flexible preconditioning technique [14] to the solution of the shifted systems. Such flexible preconditioning with a few parameters could probably cover all the shifted systems with the shift in a wide range. Numerical experiments report the effectiveness of our approach on some problems.

  • Keywords

Shifted linear systems, Arnoldi method, Flexible preconditioning.

  • AMS Subject Headings

65F10, 65Y20.

  • Copyright

COPYRIGHT: © Global Science Press

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@Article{JCM-25-522, author = {G.-D. Gu, X.-L. Zhou and Lei Lin}, title = {A Flexible Preconditioned Arnoldi Method for Shifted Linear Systems}, journal = {Journal of Computational Mathematics}, year = {2007}, volume = {25}, number = {5}, pages = {522--530}, abstract = {

We are interested in the numerical solution of the large nonsymmetric shifted linear system, $(A + \alpha I) x = b$, for many different values of the shift $\alpha$ in a wide range. We apply the Saad's flexible preconditioning technique [14] to the solution of the shifted systems. Such flexible preconditioning with a few parameters could probably cover all the shifted systems with the shift in a wide range. Numerical experiments report the effectiveness of our approach on some problems.

}, issn = {1991-7139}, doi = {https://doi.org/}, url = {http://global-sci.org/intro/article_detail/jcm/8710.html} }
TY - JOUR T1 - A Flexible Preconditioned Arnoldi Method for Shifted Linear Systems AU - G.-D. Gu, X.-L. Zhou & Lei Lin JO - Journal of Computational Mathematics VL - 5 SP - 522 EP - 530 PY - 2007 DA - 2007/10 SN - 25 DO - http://doi.org/ UR - https://global-sci.org/intro/article_detail/jcm/8710.html KW - Shifted linear systems, Arnoldi method, Flexible preconditioning. AB -

We are interested in the numerical solution of the large nonsymmetric shifted linear system, $(A + \alpha I) x = b$, for many different values of the shift $\alpha$ in a wide range. We apply the Saad's flexible preconditioning technique [14] to the solution of the shifted systems. Such flexible preconditioning with a few parameters could probably cover all the shifted systems with the shift in a wide range. Numerical experiments report the effectiveness of our approach on some problems.

G.-D. Gu, X.-L. Zhou and Lei Lin. (2007). A Flexible Preconditioned Arnoldi Method for Shifted Linear Systems. Journal of Computational Mathematics. 25 (5). 522-530. doi:
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