Improved Polynomial Bounds and Acceleration of GMRES by Solving a min-max Problem on Rectangles, and by Deflating
Numerical Analysis
2025-10-03 v2 Numerical Analysis
Abstract
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 particular, the case of positive definite A is considered. The well-known polynomial bounds are generalized to the cases considered, and then reduced to solving a min-max problem on rectangles on the complex plane. Several approaches are considered and compared. The new bounds can be improved by using specific deflation spaces and preconditioners. This in turn accelerates the convergence of GMRES. Numerical examples illustrate the results obtained.
Cite
@article{arxiv.2504.05723,
title = {Improved Polynomial Bounds and Acceleration of GMRES by Solving a min-max Problem on Rectangles, and by Deflating},
author = {Nicole Spillane and Daniel B Szyld},
journal= {arXiv preprint arXiv:2504.05723},
year = {2025}
}