An adaptive discretization for Tikhonov-Phillips regularization with a posteriori parameter selection

Summary. The aim of this paper is to describe an efficient adaptive strategy for discretizing ill-posed linear operator equations of the first kind: we consider Tikhonov-Phillips regularization

\[ x_{\alpha}^{\delta} = \left(A^{\ast}A+\alpha I\right)^{-1}A^{\ast}y^{\delta} \]

with a finite dimensional approximation \(A_n\) instead of A. We propose a sparse matrix structure which still leads to optimal convergences rates but requires substantially less scalar products for computing \(A_n\) compared with standard methods.

Authors and Affiliations

1. Universität Bremen, Fachbereich Mathematik und Informatik, Postfach 330440, 28334 Bremen, Germany , , , , , , DE

   Peter Maaß, Sergei V. Pereverzev, Ronny Ramlau & Sergei G. Solodky

Received September 16, 1998 / Revised version received August 4, 1999 / Published online August 2, 2000

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