Regularization algorithms based on total least squares

Per Christian Hansen, Dianne P. O'Leary

    Research output: Chapter in Book/Report/Conference proceedingArticle in proceedingsResearchpeer-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. Classical regularization methods, such as Tikhonov's method or truncated {\em SVD}, are not designed for problems in which both the coefficient matrix and the right-hand side are known only approximately. For this reason, we develop {\em TLS}\/-based regularization methods that take this situation into account. Here, we survey two different approaches to incorporation of regularization, or stabilization, into the {\em TLS} setting. The two methods are similar in spirit to Tikhonov regularization and truncated {\em SVD}, respectively. We analyze the regularizing properties of the methods and demonstrate by numerical examples that in certain cases with large perturbations, these new methods are able to yield more accurate regularized solutions than those produce...
    Original languageEnglish
    Title of host publicationRecent Advances in Total Least Squares Techniques and Errors-in-Variables
    EditorsSabine Van Huffel
    Place of PublicationPhiladelphia
    PublisherSociety for Industrial and Applied Mathematics
    Publication date1996
    Pages127-137
    Publication statusPublished - 1996
    EventRecent Advances in Total Least Squares Techniques and Errors-in-Variables Modeling -
    Duration: 1 Jan 1996 → …

    Conference

    ConferenceRecent Advances in Total Least Squares Techniques and Errors-in-Variables Modeling
    Period01/01/1996 → …

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