Robust Superlinear Krylov Convergence for Complex Noncoercive Compact-Equivalent Operator Preconditioners

Axelsson, Owe and Karátson, János and Magoules, Frederick (2023) Robust Superlinear Krylov Convergence for Complex Noncoercive Compact-Equivalent Operator Preconditioners. SIAM JOURNAL ON NUMERICAL ANALYSIS, 61 (2). pp. 1057-1079. ISSN 0036-1429

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Official URL: https://doi.org/10.1137/21M1466955

Abstract

Preconditioning for Krylov methods often relies on operator theory when mesh independent estimates are looked for. The goal of this paper is to contribute to the long development of the analysis of superlinear convergence of Krylov iterations when the preconditioned operator is a compact perturbation of the identity. Mesh independent superlinear convergence of GMRES and CGN iterations is derived for Galerkin solutions for complex non-Hermitian and noncoercive operators. The results are applied to noncoercive boundary value problems, including shifted Laplacian preconditioners for Helmholtz problems.

Item Type:	Article
Additional Information:	Funding Agency and Grant Number: National Research, Development and Inno-vation Office (NKFIH) [K137699, SNN125119] Funding text: Funding: This research has been supported by the National Research, Development and Inno-vation Office (NKFIH) , grants K137699 and SNN125119.
Uncontrolled Keywords:	Krylov iteration, preconditioning, non-coercive operators, mesh independence, shifted Laplace
Subjects:	Q Science / természettudomány > QA Mathematics / matematika Q Science / természettudomány > QA Mathematics / matematika > QA75 Electronic computers. Computer science / számítástechnika, számítógéptudomány
SWORD Depositor:	MTMT SWORD
Depositing User:	MTMT SWORD
Date Deposited:	24 Sep 2025 10:26
Last Modified:	24 Sep 2025 10:26
URI:	https://real.mtak.hu/id/eprint/225144

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