Iterative methods in ill-posed problems with random errors
type: Item
instance of: scholarly article
title: Iterative methods in ill-posed problems with random errors
zbMATH Open document ID: 0575.65051
published in: Automation and Remote Control
publication date: 1984-01-01T00:00:00Z
review text: For an ill-posed linear equation \(A_ 0u=f_ 0\) in a Hilbert space an iterative scheme \(u_{n+1}=u_ n-A^*A u_ n+A^*f+w_ n\), \(n\geq 0\), is applied. Here \(A-A_ 0\) and \(f-f_ 0\) are errors, and the \(w_ n\) are random errors. Under some ''smallness'' assumptions for the expectations and variances of the \(| w_ k|\) six different stopping rules are analyzed and their types of convergence (in probabilistic sense) are discussed.
Mathematics Subject Classification ID: 65J10
Mathematics Subject Classification ID: 47A50
zbMATH DE Number: 3919672
zbMATH Keywords: ill-posed problems
zbMATH Keywords: regularization
zbMATH Keywords: stopping rules
zbMATH Keywords: random errors
zbMATH Keywords: Hilbert space
zbMATH Keywords: iterative scheme
author: A. Yu. Veretennikov
reviewed by: Rudolf Gorenflo
MaRDI profile type: Publication
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description: scientific article; zbMATH DE number 3919672