Abstract
The purpose of this paper is to analyze Tikhonov regularization in general form by means of generalized SVD (GSVD) in the same spirit as SVD is used to analyze standard-form regularization. We also define a truncated GSVD solution which is of interest in its own right and which sheds light on regularization as well. In addition, our analysis gives insight into a particular numerical method for solving the general-form problem via a transformation to standard form.
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Part of this work was carried out while visiting the Mathematical Sciences Section, Oak Ridge National Laboratory, Tennessee, during the Numerical Linear Algebra Year 1987–88, and was supported by the Danish Natural Science Foundation.
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Hansen, P.C. Regularization,GSVD and truncatedGSVD . BIT 29, 491–504 (1989). https://doi.org/10.1007/BF02219234
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DOI: https://doi.org/10.1007/BF02219234