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Minimal residual-like condition with collinearity for shifted Krylov subspace methods

  • Akira ImakuraEmail author
Special Feature: Original Paper International Workshop on Eigenvalue Problems: Algorithms; Software and Applications, in Petascale Computing (EPASA2018)
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Abstract

In this paper, we consider shifted Krylov subspace methods for solving shifted linear systems. In such methods, the collinearity of the residual vectors plays a very important role. The minimal residual-like condition with collinearity for the shifted Krylov subspace methods was first proposed for the restarted shifted GMRES method by Frommer and Glässner in 1998, and it has been used for several shifted Krylov subspace methods, such as the shifted BiCGSTAB(\(\ell \)) and shifted IDR(s) methods. In this paper, we propose a novel minimal residual-like condition with collinearity for shifted Krylov subspace methods. Numerical experiments indicate that the proposed condition shows a better convergence behavior than the traditional condition.

Keywords

Shifted linear systems Shifted Krylov subspace methods Minimal residual-like condition Collinearity 

Mathematics Subject Classification

65F10 65F50 

Notes

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© The JJIAM Publishing Committee and Springer Japan KK, part of Springer Nature 2019

Authors and Affiliations

  1. 1.Faculty of Engineering, Information and SystemsUniversity of TsukubaTsukubaJapan

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