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Perturbation identities for regularized Tikhonov inverses and weighted pseudoinverses
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- Gulliksson, Mårten (author)
- Umeå universitet,Mittuniversitetet,Institutionen för teknik, fysik och matematik (-2008),Institutionen för datavetenskap
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- Wedin, P-Å (author)
- Umeå universitet,Institutionen för datavetenskap
- Wei, Yimin (author)
- (creator_code:org_t)
- 2000
- 2000
- English.
- In: Bit: numerical mathematics. - 0006-3835. ; 40:3, s. 513-523
- Journal article (peer-reviewed)
Abstract
Subject headings
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- 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.
Subject headings
- NATURVETENSKAP -- Matematik (hsv//swe)
- NATURAL SCIENCES -- Mathematics (hsv//eng)
Keyword
- Tikhonov regularization - minimum-norm - GSVD - perturbation theory - rank-deficient - pseudoinverse - filter factors
- MATHEMATICS
- MATEMATIK
Publication and Content Type
- ref (subject category)
- art (subject category)
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