Regularization of ill-posed problems with normally resolvable operators
type: Item
instance of: scholarly article
title: Regularization of ill-posed problems with normally resolvable operators
zbMATH Open document ID: 0946.65037
author: S. F. Gilyazov
author: Vladimir Morozov
published in: Computational Mathematics and Mathematical Physics
publication date: 2000-06-19T00:00:00Z
review text: The authors consider the following minimization problem in Hilbert space \(U\): \[ \min\|u\|, \quad U\subset U_f, \quad U_f= \{u\in D: Au=f\}, \] where the operator \(A\) and an element \(f\) are given approximately, i.e. \(\|A_\eta- A\|\leq \eta\), \(\|f_\delta- f\|\leq \delta\), \(0< \eta\leq \eta^*< \infty\) and \(D\) a convex, closed set from \(U\). Regularization methods for these ill-posed problems are analyzed. These methods can be used to approximate a pseudosolution with a rate of error equal to that of the initial date \(\eta\) and \(\delta\).
Mathematics Subject Classification ID: 65J10
Mathematics Subject Classification ID: 65J20
Mathematics Subject Classification ID: 47A50
Mathematics Subject Classification ID: 47A52
zbMATH DE Number: 1440449
zbMATH Keywords: ill-posed problems
zbMATH Keywords: regularization methods
zbMATH Keywords: Hilbert space
zbMATH Keywords: approximate data
zbMATH Keywords: pseudosolution
MaRDI profile type: Publication
description: scientific article; zbMATH DE number 1440449