Tikhonov Regularization and Total Least Squares

G. H. Golub, Per Christian Hansen, D. P. O'Leary

    Research output: Contribution to journalJournal articleResearchpeer-review

    Abstract

    Discretizations of inverse problems lead to systems of linear equations with a highly ill-conditioned coefficient matrix, and in order to compute stable 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.
    Original languageEnglish
    JournalSIAM Journal of Matrix Analysis and Applications
    Volume21
    Issue number1
    Pages (from-to)185-194
    ISSN0895-4798
    DOIs
    Publication statusPublished - 2000

    Keywords

    • Total least squares
    • Discrete ill-posed problems
    • Regularization
    • Bidiagonalization

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