GMRES algorithms over 35 years

•Deep insight on both sequential and parallel GMRES for linear systems.•Rich discussion on the convergence and acceleration of GMRES.•Brief account of other problems and block algorithms. This paper is about GMRES algorithms for the solution of nonsingular linear systems. We first consider basic alg...

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Vydáno v:Applied mathematics and computation Ročník 445; s. 127869
Hlavní autor: Zou, Qinmeng
Médium: Journal Article
Jazyk:angličtina
Vydáno: Elsevier Inc 15.05.2023
Témata:
Gram-Schmidt
Linear systems
Mixed precision
Parallel computing
Preconditioning
Linear systems
Parallel computing
Gram-Schmidt
65F10
Mixed precision
Preconditioning
65Y05
ISSN:0096-3003
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Popis
Shrnutí:•Deep insight on both sequential and parallel GMRES for linear systems.•Rich discussion on the convergence and acceleration of GMRES.•Brief account of other problems and block algorithms. 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.
ISSN:0096-3003
DOI:10.1016/j.amc.2023.127869