A class of nested iteration schemes for linear systems with a coefficient matrix with a dominant positive definite symmetric part
type: Item
instance of: scholarly article
title: A class of nested iteration schemes for linear systems with a coefficient matrix with a dominant positive definite symmetric part
zbMATH Open document ID: 1054.65028
DOI: 10.1023/B:NUMA.0000021766.70028.66
author: Shou-Xia Qiu
author: Owe Axelsson
author: Zhong-Zhi Bai
published in: Numerical Algorithms
publication date: 2004-08-10T00:00:00Z
review text: A class of nested splitting conjugate gradient (NSCG) methods is proposed for solving large sparse systems of linear equations with coefficient matrices with a dominant symmetric positive definite part. The NSCG method is actually an inner/outer iterative method with a particular splitting iteration as its outer iteration, and with the CG iteration as its inner iteration. The inner CG iteration itself can be further preconditioned by employing a suitable preconditioner. This naturally leads to a preconditioned NSCG (PNSCG) method. Numerical examples show that NSCG and PNSCG converge faster and more robustly to the exact solution than the generalized minimal residual (GMRES) method and its preconditioned variant, respectively.
Mathematics Subject Classification ID: 65F10
Mathematics Subject Classification ID: 65F50
Mathematics Subject Classification ID: 65F35
zbMATH DE Number: 2085902
zbMATH Keywords: inner/outer iteration
zbMATH Keywords: comparison of methods
zbMATH Keywords: GMRES method
zbMATH Keywords: Krylov subspace iterations
zbMATH Keywords: incomplete factorization
zbMATH Keywords: relaxation iteration
zbMATH Keywords: convergence
zbMATH Keywords: preconditioning
zbMATH Keywords: generalized minimal residual method
reviewed by: Liu Xinguo
describes a project that uses: GpBiCg
MaRDI profile type: Publication
full work available at URL: b:numa.0000021766.70028.66
OpenAlex ID: W2053564565
description: scientific article; zbMATH DE number 2085902