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Mathematics
Volume 13
Issue 12
10.3390/math13121953
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Article

A Randomized Q-OR Krylov Subspace Method for Solving Nonsymmetric Linear Systems

by
Gérard Meurant
Retired Researcher, 75012 Paris, France
Mathematics 2025, 13(12), 1953; https://doi.org/10.3390/math13121953
Submission received: 22 April 2025 / Revised: 4 June 2025 / Accepted: 11 June 2025 / Published: 12 June 2025
(This article belongs to the Special Issue Numerical Analysis and Scientific Computing for Applied Mathematics)
Versions Notes

Abstract

The most popular iterative methods for solving nonsymmetric linear systems are Krylov methods. Recently, an optimal Quasi-ORthogonal (Q-OR) method was introduced, which yields the same residual norms as the Generalized Minimum Residual (GMRES) method, provided GMRES is not stagnating. In this paper, we study how to introduce matrix sketching in this algorithm. It allows us to reduce the dimension of the problem in one of the main steps of the algorithm.
Keywords: linear systems; Krylov methods; Q-OR algorithm; randomization; matrix sketching linear systems; Krylov methods; Q-OR algorithm; randomization; matrix sketching

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MDPI and ACS Style

Meurant, G. A Randomized Q-OR Krylov Subspace Method for Solving Nonsymmetric Linear Systems. Mathematics 2025, 13, 1953. https://doi.org/10.3390/math13121953

AMA Style

Meurant G. A Randomized Q-OR Krylov Subspace Method for Solving Nonsymmetric Linear Systems. Mathematics. 2025; 13(12):1953. https://doi.org/10.3390/math13121953

Chicago/Turabian Style

Meurant, Gérard. 2025. "A Randomized Q-OR Krylov Subspace Method for Solving Nonsymmetric Linear Systems" Mathematics 13, no. 12: 1953. https://doi.org/10.3390/math13121953

APA Style

Meurant, G. (2025). A Randomized Q-OR Krylov Subspace Method for Solving Nonsymmetric Linear Systems. Mathematics, 13(12), 1953. https://doi.org/10.3390/math13121953

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