Iterative methods for operator equations with adjoint factorization
type: Item
instance of: scholarly article
title: Iterative methods for operator equations with adjoint factorization
zbMATH Open document ID: 0949.65025
DOI: 10.1007/BF02674600
author: A. N. Konovalov
published in: Siberian Mathematical Journal
publication date: 2000-08-30T00:00:00Z
full work available at URL: https://eudml.org/doc/120651
review text: First, the author gives a brief review of iterative methods for solving linear systems \(Au=f\) with a degenerate matrix \(A\) and \(u,f\in \mathbb{R}^n\). Next, he considers the following operator equations: \[ R^*Ru=f,\quad RR^*u=g, \tag{1} \] where \(R\: H\to H^*\) and the adjoint \(R^*\: H^*\to H\) are linear operators in finite-dimensional Euclidean spaces \(H\) and \(H^*\). Systems (1) are also degenerate. The former system in (1) can be reduced to the system \[ R^*\xi=f,\quad Ru=\xi \] which, in this article, plays the role of a basic system for constructing iterative numerical methods. An analysis of these methods is presented. It is shown that the results are applicable to the numerical solution of boundary value problems for second-order elliptic systems in the divergent form.
Mathematics Subject Classification ID: 65F10
Mathematics Subject Classification ID: 65N06
Mathematics Subject Classification ID: 35J25
zbMATH DE Number: 1498468
zbMATH Keywords: degenerate matrix
zbMATH Keywords: iterative methods
zbMATH Keywords: adjoint factorization
zbMATH Keywords: elliptic boundary value problem
zbMATH Keywords: second-order elliptic system
MaRDI profile type: Publication
cites work: Q5818478
cites work: Q3945464
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description: scientific article; zbMATH DE number 1498468