On the convergence of semiiterative methods to the Drazin inverse solution of linear equations in Banach spaces
type: Item
instance of: scholarly article
title: On the convergence of semiiterative methods to the Drazin inverse solution of linear equations in Banach spaces
zbMATH Open document ID: 0848.65043
published in: Collectanea Mathematica
publication date: 1996-11-03T00:00:00Z
full work available at URL: https://eudml.org/doc/40117
review text: We consider general semiiterative methods (SIMs) to find approximate solutions of singular linear equations of the type \(x = Tx + c\), where \(T\) is a bounded linear operator on a complex Banach space \(X\) such that its resolvent has a pole of order \(\nu_1\) at the point 1. Necessary and sufficient conditions for the convergence of SIMs to a solution of \(x = Tx + c\), where \(c\) belongs to the subspace range \({\mathcal R}(I - T)^{\nu_1}\), are established. If \(c \notin {\mathcal R} (I - T)^{\nu_1}\) sufficient conditions for the convergence to the Drazin inverse solution are described. For the class of normal operators in a Hilbert space, we analyze the convergence to the minimal norm solution and to the least squares minimal norm solution.
Mathematics Subject Classification ID: 65J10
Mathematics Subject Classification ID: 65J20
Mathematics Subject Classification ID: 47A05
Mathematics Subject Classification ID: 47A50
zbMATH DE Number: 894163
zbMATH Keywords: semiiterative methods
zbMATH Keywords: singular linear equations
zbMATH Keywords: Banach space
zbMATH Keywords: convergence
zbMATH Keywords: Drazin inverse solution
zbMATH Keywords: normal operators
zbMATH Keywords: Hilbert space
zbMATH Keywords: least squares minimal norm solution
author: Nieves Castro-González
MaRDI profile type: Publication
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description: scientific article; zbMATH DE number 894163