Perturbation identities for regularized Tikhonov inverses and weighted pseudoinverses

Gulliksson, Mårten (författare): Umeå universitet,Mittuniversitetet,Institutionen för teknik, fysik och matematik (-2008),Institutionen för datavetenskap

Wei, Yimin (författare)

(creator_code:org_t)

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Abstract Ämnesord

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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.

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