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Perturbation identities for regularized Tikhonov inverses and weighted pseudoinverses
Mid Sweden University, Faculty of Science, Technology and Media, Department of Engineering, Physics and Mathematics.
Responsible organisation
2000 (English)In: Bit: numerical mathematics, ISSN 0006-3835, Vol. 40, no 3, 513-523 p.Article in journal (Refereed) Published
Abstract [en]

e consider the perturbation analysis of two important problems for solving ill-conditioned or rank-deficient linear least squares problems. The Tikhonov regularized problem is a linear least squares problem with a regularization term balancing the size of the residual against the size of the weighted solution. The weight matrix can be a non-square matrix (usually with fewer rows than columns). The minimum-norm problem is the minimization of the size of the weighted solutions given by the set of solutions to the, possibly rank-deficient, linear least squares problem. It is well known that the solution of the Tikhonov problem tends to the minimum-norm solution as the regularization parameter of the Tikhonov problem tends to zero. Using this fact and the generalized singular value decomposition enable us to make a perturbation analysis of the minimum-norm problem with perturbation results for the Tikhonov problem. From the analysis we attain perturbation identities for Tikhonov inverses and weighted pseudoinverses.

Place, publisher, year, edition, pages
2000. Vol. 40, no 3, 513-523 p.
Keyword [en]
Tikhonov regularization - minimum-norm - GSVD - perturbation theory - rank-deficient - pseudoinverse - filter factors
National Category
Mathematics
Identifiers
URN: urn:nbn:se:miun:diva-3976Local ID: 4390OAI: oai:DiVA.org:miun-3976DiVA: diva2:29008
Available from: 2008-09-30 Created: 2009-09-21Bibliographically approved

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Gulliksson, Mårten
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