Deflation of Eigenvalues for Iterative Methods in Lattice QCD

Abstract

Work on generalizing the deflated, restarted GMRES algorithm, useful in lattice studies using stochastic noise methods, is reported. We first show how the multi-mass extension of deflated GMRES can be implemented. We then give a deflated GMRES method that can be used on multiple right-hand sides of $Ax=b$ in an efficient manner. We also discuss and give numerical results on the possibilty of combining deflated GMRES for the first right hand side with a deflated BiCGStab algorithm for the subsequent right hand sides.