4 papers · 1 filter
Do you precondition on the left or on the right?
Nicole Spillane, Pierre Matalon, Daniel B Szyld
This work is a follow-up to a poster that was presented at the DD29 conference. Participants were asked the question: ``Do you precondition on the left or on the right?''. Here we…
Any nonincreasing convergence curves are simultaneously possible for GMRES and weighted GMRES, as well as for left and right preconditioned GMRES
Pierre Matalon, Nicole Spillane
The convergence of the GMRES linear solver is notoriously hard to predict. A particularly enlightening result by [Greenbaum, Pták, Strakoš, 1996] is that, given any convergence cur…
Improved Polynomial Bounds and Acceleration of GMRES by Solving a min-max Problem on Rectangles, and by Deflating
Nicole Spillane, Daniel B Szyld
Polynomial convergence bounds are considered for left, right, and split preconditioned GMRES. They include the cases of Weighted and Deflated GMRES for a linear system Ax = b. In p…
New Convergence Analysis of GMRES with Weighted Norms, Preconditioning and Deflation, Leading to a New Deflation Space
Nicole Spillane, Daniel B Szyld
New convergence bounds are presented for weighted, preconditioned, and deflated GMRES for the solution of large, sparse, non-Hermitian linear systems. These bounds are given for th…