Deflated BiCGStab for linear equations in QCD problems

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dc.creatorAbdel-Rehim, Abdou
dc.creatorMorgan, Ronald B.
dc.creatorWilcox, Walter
dc.date2007-10-10
dc.date.accessioned2026-07-07T11:53:29Z
dc.date.available2026-07-07T11:53:29Z
dc.descriptionThe large systems of complex linear equations that are generated in QCD problems often have multiple right-hand sides (for multiple sources) and multiple shifts (for multiple masses). Deflated GMRES methods have previously been developed for solving multiple right-hand sides. Eigenvectors are generated during solution of the first right-hand side and used to speed up convergence for the other right-hand sides. Here we discuss deflating non-restarted methods such as BiCGStab. For effective deflation, both left and right eigenvectors are needed. Fortunately, with the Wilson matrix, left eigenvectors can be derived from the right eigenvectors. We demonstrate for difficult problems with kappa near kappa_c that deflating eigenvalues can significantly improve BiCGStab. We also will look at improving solution of twisted mass problems with multiple shifts. Projecting over previous solutions is an easy way to reduce the work needed.
dc.description7 pages, 4 figures, presented at the XXV International Symposium on Lattice Field Theory, 30 July - 4 August 2007, Regensburg, Germany
dc.identifierhttps://arxiv.org/abs/0710.1988
dc.identifierhttp://arxiv.org/abs/0710.1988
dc.identifierPoSLAT2007:026,2007
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/204555
dc.subjectHigh Energy Physics - Lattice
dc.titleDeflated BiCGStab for linear equations in QCD problems
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