A new Tikhonov regularization method |
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Authors: | Martin Fuhry Lothar Reichel |
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Institution: | (1) Department of Mathematics, University of Bologna, Piazza Porta S. Donato 5, 40127 Bologna, Italy;(2) Department of Mathematical Sciences, Kent State University, Kent, OH 44242, USA;(3) CIRAM Department of Mathematics, University of Bologna, via Saragozza 8, 40123 Bologna, Italy |
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Abstract: | The numerical solution of linear discrete ill-posed problems typically requires regularization, i.e., replacement of the available
ill-conditioned problem by a nearby better conditioned one. The most popular regularization methods for problems of small
to moderate size, which allow evaluation of the singular value decomposition of the matrix defining the problem, are the truncated
singular value decomposition and Tikhonov regularization. The present paper proposes a novel choice of regularization matrix
for Tikhonov regularization that bridges the gap between Tikhonov regularization and truncated singular value decomposition.
Computed examples illustrate the benefit of the proposed method. |
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Keywords: | |
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