Tikhonov Regularization and Total Least Squares

TitleTikhonov Regularization and Total Least Squares
Publication TypeJournal Articles
Year of Publication1999
AuthorsGolub GH, Hansen P C, O'Leary DP
JournalSIAM Journal on Matrix Analysis and Applications
Pagination185 - 194
Date Published1999///
Keywordsbidiagonalization, discrete ill-posed problems, regularization, total least squares

Discretizations of inverse problems lead to systems of linear equations with a highly ill-conditioned coefficient matrix, and in order to computestable solutions to these systems it is necessary to apply regularization methods. We show how Tikhonov's regularization method, which in its original formulation involves a least squares problem, can be recast in a total least squares formulation suited for problems in which both the coefficient matrix and the right-hand side are known only approximately. We analyze the regularizing properties of this method and demonstrate by a numerical example that, in certain cases with large perturbations, the new method is superior to standard regularization methods.