Volume 7, Issue 3
Restarted Full Orthogonalization Method with Deflation for Shifted Linear Systems

Jun-Feng Yin & Guo-Jian Yin

Numer. Math. Theor. Meth. Appl., 7 (2014), pp. 399-412.

Published online: 2014-07

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  • Abstract

In this paper, we study shifted restated full orthogonalization method with deflation for simultaneously solving a number of shifted systems of linear equations. Theoretical analysis shows that with the deflation technique, the new residual of shifted restarted FOM is still collinear with each other. Hence, the new approach can solve the shifted systems simultaneously based on the same Krylov subspace. Numerical experiments show that the deflation technique can significantly improve the convergence performance of shifted restarted FOM.

  • Keywords

Shifted linear systems, full orthogonalization method, restarted Arnoldi process, deflation, collinear.

  • AMS Subject Headings

65F10, 65F15, 15A06, 15A18

  • Copyright

COPYRIGHT: © Global Science Press

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@Article{NMTMA-7-399, author = {}, title = {Restarted Full Orthogonalization Method with Deflation for Shifted Linear Systems}, journal = {Numerical Mathematics: Theory, Methods and Applications}, year = {2014}, volume = {7}, number = {3}, pages = {399--412}, abstract = {

In this paper, we study shifted restated full orthogonalization method with deflation for simultaneously solving a number of shifted systems of linear equations. Theoretical analysis shows that with the deflation technique, the new residual of shifted restarted FOM is still collinear with each other. Hence, the new approach can solve the shifted systems simultaneously based on the same Krylov subspace. Numerical experiments show that the deflation technique can significantly improve the convergence performance of shifted restarted FOM.

}, issn = {2079-7338}, doi = {https://doi.org/10.4208/nmtma.2014.y13010}, url = {http://global-sci.org/intro/article_detail/nmtma/5881.html} }
TY - JOUR T1 - Restarted Full Orthogonalization Method with Deflation for Shifted Linear Systems JO - Numerical Mathematics: Theory, Methods and Applications VL - 3 SP - 399 EP - 412 PY - 2014 DA - 2014/07 SN - 7 DO - http://doi.org/10.4208/nmtma.2014.y13010 UR - https://global-sci.org/intro/article_detail/nmtma/5881.html KW - Shifted linear systems, full orthogonalization method, restarted Arnoldi process, deflation, collinear. AB -

In this paper, we study shifted restated full orthogonalization method with deflation for simultaneously solving a number of shifted systems of linear equations. Theoretical analysis shows that with the deflation technique, the new residual of shifted restarted FOM is still collinear with each other. Hence, the new approach can solve the shifted systems simultaneously based on the same Krylov subspace. Numerical experiments show that the deflation technique can significantly improve the convergence performance of shifted restarted FOM.

Jun-Feng Yin & Guo-Jian Yin. (2020). Restarted Full Orthogonalization Method with Deflation for Shifted Linear Systems. Numerical Mathematics: Theory, Methods and Applications. 7 (3). 399-412. doi:10.4208/nmtma.2014.y13010
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