An efficient method for constructing an ILU preconditioner for solving large sparse nonsymmetric linear systems by the GMRES method
type: Item
instance of: scholarly article
title: An efficient method for constructing an ILU preconditioner for solving large sparse nonsymmetric linear systems by the GMRES method
zbMATH Open document ID: 1050.65050
DOI: 10.1016/S0898-1221(03)00154-8
publication date: 2004-08-06T00:00:00Z
review text: An incomplete LU decompositions (ILU) of a sparse \(n \times n\) matrix \(A\) is an LU decomposition which neglects entries not contained in a set \(P \subset \{1, \dots, n\} \times \{1, \dots, n\}\) during the elimination process. This limits the fill-in in the triangular factors \(L\) and \(U\) and may drastically reduce the computational requirements compared to a complete LU decomposition. Although an ILU itself does not admit the accurate solution of a system of linear equations, it is often successfully used as a preconditioner in iterative methods, such as GMRES or BiCG. The authors consider sets \(P\) that are determined by the generic nonzero pattern of the matrix \(A+A^2+\cdots A^m\), giving rise to ILU(\(m\)). It is proposed to use the Floyd-Warshall algorithm for constructing \(P\). Some numerical experiments illustrate the preconditioning capabilities of ILU(\(m\)) in combination with GMRES. However, there are no numerical comparisons to other ILU preconditioners, such as the very similar ILU(\(p\)) described in \textit{Y. Saad}'s book [Iterative methods for sparse linear systems (2nd ed., SIAM, Philadelphia) (2003; Zbl 1031.65046)].
reviewed by: Daniel Kressner
Mathematics Subject Classification ID: 65F35
Mathematics Subject Classification ID: 65F10
Mathematics Subject Classification ID: 65F50
zbMATH DE Number: 2082297
zbMATH Keywords: ILU
zbMATH Keywords: preconditioning
zbMATH Keywords: GMRES
zbMATH Keywords: Krylov subspace
zbMATH Keywords: Boolean matrix
zbMATH Keywords: incomplete LU decompositions
zbMATH Keywords: sparse matrix
zbMATH Keywords: iterative methods
zbMATH Keywords: Floyd-Warshall algorithm
zbMATH Keywords: numerical experiments
author: R. C. Mittal
author: Ahmad Al-Kurdi
describes a project that uses: CGS
describes a project that uses: symrcm
describes a project that uses: NAPACK
MaRDI profile type: Publication
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full work available at URL: s0898-1221(03)00154-8
OpenAlex ID: W1971722861
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published in: Computers & Mathematics with Applications
description: scientific article; zbMATH DE number 2082297