The 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.Comment: 7 pages, 4 figures, presented at the XXV International Symposium on
Lattice Field Theory, 30 July - 4 August 2007, Regensburg, German
