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

Gérard Meurant ()
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Gérard Meurant: Retired Researcher, 75012 Paris, France

Mathematics, 2025, vol. 13, issue 12, 1-10

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 (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2025
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