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Persistent URL http://purl.org/net/epubs/work/40486
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Record Id 40486
Title A note on GMRES preconditioned by a perturbed LDL(T) decomposition with static pivoting
Abstract A strict adherence to threshold pivoting in the direct solution of symmetric indefinite problems can result in substantially more work and storage than forecast by an sparse analysis of the symmetric problem. One way of avoiding this is to use static pivoting where the data structures and pivoting sequence generated by the analysis are respected and pivots that would otherwise be very small are replaced by a user defined quantity. This can give a stable factorization but of a perturbed matrix. The conventional way of solving the sparse linear system is then to use iterative refinement (IR) but there are cases where this fails to converge. In this paper, we discuss the use of more robust iterative methods, namely GMRES and FGMRES. We show both theoretically and experimentally that both these approaches are more robust than IR and furthermore that FGMRES is far more robust than GMRES and that, under reasonable hypotheses, FGMRES is backward stable. We also show how restarted variants can be beneficial although again the GMRES variant is not as robust as FGMRES.
Organisation CCLRC , CSE , CSE-NAG
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Language English (EN)
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Journal Article SIAM J Sci Comput 29 (2007): 2024-2044. doi:10.1137/060661545 2007
Report RAL Technical Reports RAL-TR-2006-007. 2006. adgpRAL2006007.pdf 2006