Regularization of ill-posed problems by stochastic iteration procedures in the mean
type: Item
instance of: scholarly article
title: Regularization of ill-posed problems by stochastic iteration procedures in the mean
zbMATH Open document ID: 0623.65062
published in: Automation and Remote Control
publication date: 1986-01-01T00:00:00Z
review text: The author studies a general iteration method of Vainikko for an ill- posed linear operator equation in Hilbert space with approximately given operator and data. In addition, it is assumed that independent random errors influence each iteration. A stopping rule for the iteration which depends on knowledge of an upper bound for the true solution and bounds for the error in the data and operator as well as the satisfaction of a certain inequality involving the expected norm of the random errors, is proposed. The author proves that the approximate solution using this stopping rule converges in expectation to the exact solution as the various error levels go to zero, i.e., the method using the stopping rule is a regularization procedure in the sense of Tikhonov.
Mathematics Subject Classification ID: 65J10
Mathematics Subject Classification ID: 47A50
zbMATH DE Number: 4011803
zbMATH Keywords: stochastic iteration
zbMATH Keywords: linear ill-posed problem
zbMATH Keywords: Vainikko method
zbMATH Keywords: Tikhonov regularization
zbMATH Keywords: convergence
zbMATH Keywords: iteration method
zbMATH Keywords: Hilbert space
zbMATH Keywords: random errors
zbMATH Keywords: stopping rule
author: A. Yu. Veretennikov
reviewed by: Charles W. Groetsch
MaRDI profile type: Publication
description: scientific article; zbMATH DE number 4011803