Tikhonov regularization and the L-curve for large discrete ill-posed problems
type: Item
instance of: scholarly article
title: Tikhonov regularization and the L-curve for large discrete ill-posed problems
zbMATH Open document ID: 0977.65030
DOI: 10.1016/S0377-0427(00)00414-3
published in: Journal of Computational and Applied Mathematics
publication date: 2002-01-21T00:00:00Z
review text: The problem is to solve very ill-conditioned large systems of linear algebraic equations obtained by discretization of linear inverse problems. For solving such ill-posed problems the Tikhonov regularization method is used. The total cost of an regularization method is to a large extent determined by the amount of the computational work needed for determining a suitable regularization parameter. The authors survey available iterative methods, and develope new ones, based on the L-curve method, in particular, on the L-ribbon method for the determination a proper value for the regularization parameter. They discuss iterative methods based on the Laczos bidiagonalization and the Arnoldi process for the computation of approximate values for \(\mu\) that corresponds to the value of the regularization parameter obtainable by the L-curve criterion. Computed examples are presented.
Mathematics Subject Classification ID: 65F22
zbMATH DE Number: 1546557
zbMATH Keywords: ill-conditioned large systems of linear algebraic equations
zbMATH Keywords: linear inverse problems
zbMATH Keywords: ill-posed problems
zbMATH Keywords: Tikhonov regularization method
zbMATH Keywords: iterative methods
zbMATH Keywords: L-curve method
zbMATH Keywords: L-ribbon method
zbMATH Keywords: regularization parameter
zbMATH Keywords: Laczos bidiagonalization
zbMATH Keywords: Arnoldi process
author: Daniela Calvetti
author: Serena Morigi
author: Lothar Reichel
author: Fiorella Sgallari
reviewed by: Otu Vaarmann
describes a project that uses: CRAIG
describes a project that uses: LAPACK
describes a project that uses: Regularization tools
describes a project that uses: BLAS
describes a project that uses: SPOOLES
describes a project that uses: LSQR
describes a project that uses: ScaLAPACK
MaRDI profile type: Publication
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description: scientific article; zbMATH DE number 1546557