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A FLEXIBLE PRECONDITIONED ARNOLDI METHOD FOR shifted linear systems

Journal of Computational Mathematics 2007年第5期25卷 522-530页

作者： G.-D. Gu X.-L. Zhou Lei Lin Department of Applied Mathematics Shanghai University of Finance and Economics Shanghai 200433 China Department of Mathematics Shanghai University Shanghai 200436 China

We are interested in the numerical solution of the large nonsymmetric shifted linear system, （A ＋ αI）x -= b, for many different values of the shift a in a wide range. We apply the Saad＇s flexible preconditioning technique 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.

关键词： shifted linear systems 65F10 65Y20. Arnoldi method Flexible preconditioning

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Restarted Full Orthogonalization Method with Deflation for shifted linear systems

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Numerical Mathematics(Theory,Methods and Applications) 2014年第3期7卷 399-412页

作者： Jun-Feng Yin Guo-Jian Yin Department of Mathematics Tongji University1239 Siping RoadShanghai 200092P.R.China Department of Mathematics The Chinese University of Hong KongShatinNTHong Kong

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

关键词： shifted linear systems full orthogonalization method restarted Arnoldi process deflation collinear

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An Efficient Variant of the Restarted shifted GMRES Method for Solving shifted linear systems

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Journal of Mathematical Research with Applications 2013年第2期33卷 127-141页

作者： Akira IMAKURA Tomohiro SOGABE Shaoliang ZHANG Center for Computational Sciences University of Tsukuba Graduate School of Information Science and Technology Aichi Prefectural University Graduate School of Engineering Nagoya University

We investigate the restart of the Restarted shifted GMRES method for solving shifted linear *** the variant of the GMRES(m) method with the unfixed update has been proposed to improve the convergence of the GMRES(m) method for solving linear systems,and shown to have an efficient convergence *** this paper,by applying the unfixed update to the Restarted shifted GMRES method,we propose a variant of the Restarted shifted GMRES *** show a potentiality for efficient convergence within the variant by some numerical results.

关键词： shifted linear systems the Restarted shifted GMRES method restart techniques.

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