A new Tikhonov regularization method

A new Tikhonov regularization method

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Article ID: iaor2012937
Volume: 59
Issue: 3
Start Page Number: 433
End Page Number: 445
Publication Date: Mar 2012
Journal: Numerical Algorithms
Authors: ,
Keywords: decomposition, regularisation techniques
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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