Multilevel algorithms for ill-posed problems
type: Item
instance of: scholarly article
title: Multilevel algorithms for ill-posed problems
zbMATH Open document ID: 0768.65091
DOI: 10.1007/BF01385512
author: J. Thomas King
published in: Numerische Mathematik
publication date: 1993-02-08T00:00:00Z
full work available at URL: https://eudml.org/doc/133624
review text: While the theory of multilevel algorithms is well developed for well- posed problems, this is one of the first papers studying multilevel algorithms for (linear) ill-posed problems. The author considers the weak form of Tikhonov regularization on the (finite dimensional) range space, constructs a multilevel operator on this finite dimensional space and gives error estimates with respect to the bilinear form corresponding to Tikhonov regularization. This multilevel operator is then used as a preconditioner for the Landweber and the conjugate gradient methods. The abstract results are carefully illustrated by numerical examples, namely the first kind integral equations corresponding to computing the second derivative and to the sideways heat equation, respectively.
reviewed by: Heinz W. Engl
Mathematics Subject Classification ID: 65R20
Mathematics Subject Classification ID: 65R30
Mathematics Subject Classification ID: 45B05
zbMATH DE Number: 118291
zbMATH Keywords: first kind integral equations
zbMATH Keywords: Landweber method
zbMATH Keywords: multilevel algorithms
zbMATH Keywords: ill-posed problems
zbMATH Keywords: Tikhonov regularization
zbMATH Keywords: error estimates
zbMATH Keywords: preconditioner
zbMATH Keywords: conjugate gradient methods
zbMATH Keywords: numerical examples
zbMATH Keywords: heat equation
MaRDI profile type: Publication
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OpenAlex ID: W1971270535
description: scientific article; zbMATH DE number 118291