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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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
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Abstract	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.
AbstractList	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.
Author	Lampe, Jörg Voss, Heinrich Reichel, Lothar
Author_xml	– sequence: 1 givenname: Jörg surname: Lampe fullname: Lampe, Jörg email: joerg.lampe@tu-harburg.de organization: Institute of Numerical Simulation, Hamburg University of Technology, D-21071 Hamburg, Germany – sequence: 2 givenname: Lothar surname: Reichel fullname: Reichel, Lothar email: reichel@math.kent.edu organization: Department of Mathematical Sciences, Kent State University, Kent, OH 44242, USA – sequence: 3 givenname: Heinrich surname: Voss fullname: Voss, Heinrich email: voss@tu-harburg.de organization: Institute of Numerical Simulation, Hamburg University of Technology, D-21071 Hamburg, Germany
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Keywords	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
Language	English
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SubjectTerms	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
Title	Large-scale Tikhonov regularization via reduction by orthogonal projection
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