Large-scale Tikhonov regularization via reduction by orthogonal projection

This paper presents a new approach to computing an approximate solution of Tikhonov-regularized large-scale ill-posed least-squares problems with a general regularization matrix. The iterative method applies a sequence of projections onto generalized Krylov subspaces. A suitable value of the regular...

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Bibliographic Details
Published in:Linear algebra and its applications Vol. 436; no. 8; pp. 2845 - 2865
Main Authors: Lampe, Jörg, Reichel, Lothar, Voss, Heinrich
Format: Journal Article
Language:English
Published: Amsterdam Elsevier Inc 15.04.2012
Elsevier
Subjects:
Algebra
Discrepancy principle
Exact sciences and technology
General-form Tikhonov regularization
Ill-posedness
Least squares
Linear and multilinear algebra, matrix theory
Mathematics
Numerical analysis
Numerical analysis. Scientific computation
Numerical approximation
Sciences and techniques of general use
General-form Tikhonov regularization
Discrepancy principle
65F22
65F30
Ill-posedness
Least squares
65F15
Krylov subspace method
Iterative method
Generalized
Orthogonal projection
III-posedness
Least squares method
Ill posed problem
Eigenvalue problem
Large scale
Regularization
ISSN:0024-3795
Online Access:Get full text
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Summary:This paper presents a new approach to computing an approximate solution of Tikhonov-regularized large-scale ill-posed least-squares problems with a general regularization matrix. The iterative method applies a sequence of projections onto generalized Krylov subspaces. A suitable value of the regularization parameter is determined by the discrepancy principle.
ISSN:0024-3795
DOI:10.1016/j.laa.2011.07.019