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Abstract
We consider the computation of a few eigenvectors and corresponding eigenvalues of a large sparse nonsymmetric matrix using shiftinvert Arnoldi's method with and without implicit restarts. For the inner iterations we use preconditioned GMRES as the inexact iterative solver. The costs of the solves are measured by the number of inner iterations needed by the iterative solver at each outer step of the algorithm. We first extend the relaxation strategy developed by Simoncini [SIAM J. Numer. Anal., 43 (2005), pp. 11551174] to implicitly restarted Arnoldi's method, which yields an improvement in the overall costs of the method. Secondly, we apply a new preconditioning strategy to the inner solver. We show that small rank changes to the preconditioner can produce significant savings in the total number of iterations. The combination of the new preconditioner with the relaxation strategy in implicitly restarted Arnoldi produces enhancement in the overall costs of around 50 percent in the examples considered here. Numerical experiments illustrate the theory throughout the paper.
Original language  English 

Pages (fromto)  942969 
Number of pages  28 
Journal  SIAM Journal On Matrix Analysis and Applications (SIMAX) 
Volume  31 
Issue number  3 
Early online date  11 Aug 2009 
DOIs  
Publication status  Published  2010 
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Dive into the research topics of 'Shiftinvert Arnoldi's method with preconditioned iterative solves'. Together they form a unique fingerprint.Projects
 1 Finished

THEORY AND TOOLS FOR COMPLEX BIOLOGICAL SYSTEMS
Engineering and Physical Sciences Research Council
1/11/07 → 31/10/10
Project: Research council