Using approximate inverses in algebraic multilevel methods
type: Item
instance of: scholarly article
title: Using approximate inverses in algebraic multilevel methods
zbMATH Open document ID: 0911.65027
author: Yvan Notay
published in: Numerische Mathematik
publication date: 1999-03-02T00:00:00Z
review text: This paper deals with the iterative solution of large sparse symmetric positive definite systems. The author investigates preconditioning techniques of the two-level type that are based on a block factorization of the system matrix. Whereas the basic scheme assumes an exact inversion of the submatrix related to the first block of unknowns, the author analyzes the effect of using an approximate inverse instead. Derived condition number estimates are valid for any type of approximation of the Schur complement and do not assume the use of the hierarchical basis. They show that the two-level methods are stable when using approximate inverses based on modified ILU techniques, or explicit inverses that meet some row-sum criterion. On the other hand, the author brings to the light that use of standard approximate inverses based on convergent splittings can have a dramatic effect on the convergence rate. These conclusions are numerically illustrated on some examples.
Mathematics Subject Classification ID: 65F10
Mathematics Subject Classification ID: 65F35
Mathematics Subject Classification ID: 65N55
Mathematics Subject Classification ID: 65F50
zbMATH DE Number: 1228453
zbMATH Keywords: iterative solution
zbMATH Keywords: large sparse symmetric positive definite systems
zbMATH Keywords: algebraic multilevel methods
zbMATH Keywords: numerical examples
zbMATH Keywords: preconditioning
zbMATH Keywords: approximate inverse
zbMATH Keywords: condition number
zbMATH Keywords: Schur complement
zbMATH Keywords: convergence rate
reviewed by: Karel Najzar
MaRDI profile type: Publication
full work available at URL: s002110050373
OpenAlex ID: W2016886601
DOI: 10.1007/S002110050373
description: scientific article; zbMATH DE number 1228453