GMRES algorithms over 35 years
Qinmeng Zou
TL;DR
This paper reviews 35 years of GMRES algorithms, analyzing their convergence, acceleration strategies, parallel implementations, and applications to various challenging linear systems.
Contribution
It provides a comprehensive overview of GMRES developments, including new acceleration and parallelization techniques for complex systems.
Findings
Convergence properties of basic GMRES algorithms analyzed.
Effective acceleration strategies for challenging systems discussed.
Parallel algorithms improve computational efficiency for large-scale problems.
Abstract
This paper is about GMRES algorithms for the solution of nonsingular linear systems. We first consider basic algorithms and study their convergence. We then focus on acceleration strategies and parallel algorithms that are useful for solving challenging systems. We also briefly discuss other problems, such as systems with multiple right-hand sides, shifted systems, and singular systems.
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Taxonomy
TopicsMatrix Theory and Algorithms · Numerical methods for differential equations · Advanced Optimization Algorithms Research