scholarly journals Tikhonov-regularization of ill-posed linear operator equations on closed convex sets

1988 ◽  
Vol 53 (3) ◽  
pp. 304-320 ◽  
Author(s):  
A Neubauer
Keyword(s):  
Linear Operator ◽  
Tikhonov Regularization ◽  
Convex Sets ◽  
Operator Equations ◽  
Ill Posed ◽  
Linear Operator Equations

A Variant of Projection-Regularization Method for Ill-Posed Linear Operator Equations

2020 ◽  
pp. 2150008
Author(s):  
Bechouat Tahar ◽  
Boussetila Nadjib ◽  
Rebbani Faouzia
Keyword(s):  
Approximate Solution ◽  
Linear Operator ◽  
Tikhonov Regularization ◽  
Hilbert Spaces ◽  
Regularization Method ◽  
Tikhonov Regularization Method ◽  
Operator Equations ◽  
Ill Posed ◽  
Rank Approximation ◽  
Linear Operator Equations

In this paper, we report on a strategy for computing the numerical approximate solution for a class of ill-posed operator equations in Hilbert spaces: [Formula: see text]. This approach is a combination of Tikhonov regularization method and the finite rank approximation of [Formula: see text]. Finally, numerical results are given to show the effectiveness of this method.

Ill-Posed Linear Operator Equations

2000 ◽  
pp. 31-48 ◽  
Author(s):  
Heinz W. Engl ◽  
Martin Hanke ◽  
Andreas Neubauer
Keyword(s):  
Linear Operator ◽  
Operator Equations ◽  
Ill Posed ◽  
Linear Operator Equations

scholarly journals Morozov’s Discrepancy Principle For The Tikhonov Regularization Of Exponentially Ill-Posed Problems

2008 ◽  
Vol 8 (1) ◽  
pp. 86-98 ◽  
Author(s):  
S.G. SOLODKY ◽  
A. MOSENTSOVA
Keyword(s):  
Tikhonov Regularization ◽  
Optimal Order ◽  
Discrepancy Principle ◽  
Operator Equations ◽  
Order Of Accuracy ◽  
Finite Dimensional ◽  
Dimensional Version ◽  
Ill Posed ◽  
Linear Operator Equations ◽  
Morozov’S Discrepancy Principle

Abstract The problem of approximate solution of severely ill-posed problems given in the form of linear operator equations of the first kind with approximately known right-hand sides was considered. We have studied a strategy for solving this type of problems, which consists in combinating of Morozov’s discrepancy principle and a finite-dimensional version of the Tikhonov regularization. It is shown that this combination provides an optimal order of accuracy on source sets

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