New Convergence Analysis of GMRES with Weighted Norms, Preconditioning and Deflation, Leading to a New Deflation Space - Institut Polytechnique de Paris Access content directly
Preprints, Working Papers, ... Year : 2023

New Convergence Analysis of GMRES with Weighted Norms, Preconditioning and Deflation, Leading to a New Deflation Space

Abstract

New convergence bounds are presented for weighted, preconditioned, and deflated GMRES for the solution of large, sparse, non-Hermitian linear systems. These bounds are given for the case when the Hermitian part of the coefficient matrix is positive definite, the preconditioner is Hermitian positive definite, and the weight is equal to the preconditioner. The new bounds are a novel contribution in and of themselves. In addition, they are sufficiently explicit to indicate how to choose the preconditioner and the deflation space to accelerate the convergence. One such choice of deflating space is presented, and numerical experiments illustrate the effectiveness of such space.
Fichier principal
Vignette du fichier
vHal.pdf (3.3 Mo) Télécharger le fichier
Origin Files produced by the author(s)

Dates and versions

hal-04328504 , version 1 (11-12-2023)
hal-04328504 , version 2 (07-06-2024)

Identifiers

Cite

Nicole Spillane, Daniel B Szyld. New Convergence Analysis of GMRES with Weighted Norms, Preconditioning and Deflation, Leading to a New Deflation Space. 2023. ⟨hal-04328504v2⟩
32 View
24 Download

Altmetric

Share

Gmail Mastodon Facebook X LinkedIn More