The cycle-convergence of restarted GMRES for normal matrices is sublinear
Eugene Vecharynski, Julien Langou
TL;DR
This paper proves that the convergence rate of restarted GMRES for solving linear systems with normal matrices is sublinear, providing insights into its efficiency and limitations.
Contribution
It establishes the sublinear cycle-convergence behavior of restarted GMRES specifically for normal matrices, a novel theoretical result.
Findings
Proves sublinear cycle-convergence for restarted GMRES with normal matrices
Provides theoretical insight into GMRES efficiency for normal systems
Enhances understanding of iterative solver convergence properties
Abstract
We prove that the cycle-convergence of the restarted GMRES applied to a system of linear equations with a normal coefficient matrix is sublinear.
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Taxonomy
TopicsMatrix Theory and Algorithms · Blind Source Separation Techniques · Optical Network Technologies