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Perturbation identities for regularized Tikhonov inverses and weighted pseudoinversesPrimeFaces.cw("AccordionPanel","widget_formSmash_some",{id:"formSmash:some",widgetVar:"widget_formSmash_some",multiple:true}); PrimeFaces.cw("AccordionPanel","widget_formSmash_all",{id:"formSmash:all",widgetVar:"widget_formSmash_all",multiple:true});
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PrimeFaces.cw("AccordionPanel","widget_formSmash_responsibleOrgs",{id:"formSmash:responsibleOrgs",widgetVar:"widget_formSmash_responsibleOrgs",multiple:true}); 2000 (English)In: Bit, Vol. 40, no 3, 513-523 p.Article in journal (Refereed) Published
##### Abstract [en]

##### Place, publisher, year, edition, pages

2000. Vol. 40, no 3, 513-523 p.
##### Identifiers

URN: urn:nbn:se:umu:diva-21944ISBN: 0006-3835OAI: oai:DiVA.org:umu-21944DiVA: diva2:212202
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Available from: 2009-04-21 Created: 2009-04-21 Last updated: 2009-04-21

We 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.

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