Circulant-block preconditioners for solving ordinary differential equations.
type: Item
instance of: scholarly article
title: Circulant-block preconditioners for solving ordinary differential equations.
zbMATH Open document ID: 1044.65062
DOI: 10.1016/S0096-3003(02)00237-0
author: Xiao-Qing Jin
author: Li-li Song
author: Vai-Kuong Sin
published in: Applied Mathematics and Computation
publication date: 2003-09-09T00:00:00Z
review text: Solving linear initial value problems of ordinary differential equations by boundary value methods requires the solution of non-symmetric, large and sparse linear systems. A circulant-block preconditoner for the generalized minimal residual method is proposed to solve these systems. The operation costs and the convergence rate are investigated. The proposed preconditioner is compared with \textit{D. Bertaccini}'s [SIAM J. Sci. Comput. 22, No. 3, 767--786 (2000; Zbl 0976.65071)] -- and strong-type block-circulant -- preconditioners and a block-circulant-circulant-block preconditioner. The two numerical experiments show the advantage of the new preconditioner.
reviewed by: René Lamour
Mathematics Subject Classification ID: 65L05
Mathematics Subject Classification ID: 34A30
Mathematics Subject Classification ID: 65F10
Mathematics Subject Classification ID: 65F35
zbMATH DE Number: 1978092
zbMATH Keywords: boundary value method
zbMATH Keywords: generalized minimal residual method
zbMATH Keywords: circulant-block preconditioner
zbMATH Keywords: EMRES method
zbMATH Keywords: linear initial value problems
zbMATH Keywords: sparse linear systems
zbMATH Keywords: convergence
zbMATH Keywords: numerical experiments
MaRDI profile type: Publication
cites work: A Circulant Preconditioner for the Systems of LMF-Based ODE Codes
cites work: Q4393432
cites work: A Family of Block Preconditioners for Block Systems
cites work: Conjugate Gradient Methods for Toeplitz Systems
cites work: Strang-type preconditioners for systems of LMF-based ODE codes
cites work: Q4002473
cites work: BCCB preconditioners for systems of BVM‐based numerical integrators
cites work: GMRES: A Generalized Minimal Residual Algorithm for Solving Nonsymmetric Linear Systems
cites work: Bi-CGSTAB: A Fast and Smoothly Converging Variant of Bi-CG for the Solution of Nonsymmetric Linear Systems
description: scientific article; zbMATH DE number 1978092