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Restarted Full Orthogonalization Method with Deflation for Shifted Linear Systems

Published online by Cambridge University Press:  28 May 2015

Jun-Feng Yin  and
Guo-Jian Yin
Jun-Feng Yin*
Affiliation:
Department of Mathematics, Tongji University, 1239 Siping Road, Shanghai 200092, P. R. China
Guo-Jian Yin*
Affiliation:
Department of Mathematics, Tongji University, 1239 Siping Road, Shanghai 200092, P. R. China
*
Corresponding author.Email address:yinjf@tongji.edu.cn
Corresponding author.Email address:gjyin@math.cuhk.edu.hk
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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

65F1065F1515A0615A18Shifted linear systemsfull orthogonalization methodrestarted Arnoldi processdeflationcollinear
Type
Research Article
Information
Numerical Mathematics: Theory, Methods and Applications , Volume 7 , Issue 3 , August 2014 , pp. 399 - 412
Copyright
Copyright © Global Science Press Limited 2014

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