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A Regularized Total Least Squares Algorithm

In: Total Least Squares and Errors-in-Variables Modeling

Author

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  • Hongbin Guo

    (Arizona State University, Department of Mathematics)

  • Rosemary A. Renaut

    (Arizona State University, Department of Mathematics)

Abstract

Error-contaminated systems A x ≈ b, for which A is ill-conditioned, are considered. Such systems may be solved using Tikhonov-like regularized total least squares (R-TLS) methods. Golub et al, 1999, presented a direct algorithm for the solution of the Lagrange multiplier formulation for the R-TLS problem. Here we present a parameter independent algorithm for the approximate R-TLS solution. The algorithm, which utilizes the shifted inverse power method, relies only on a prescribed estimate for the regularization constraint condition and does not require the specification of other regularization parameters. An extension of the algorithm for nonsmooth solutions is also presented.

Suggested Citation

  • Hongbin Guo & Rosemary A. Renaut, 2002. "A Regularized Total Least Squares Algorithm," Springer Books, in: Sabine Van Huffel & Philippe Lemmerling (ed.), Total Least Squares and Errors-in-Variables Modeling, pages 57-66, Springer.
    • Handle: RePEc:spr:sprchp:978-94-017-3552-0_6
    DOI: 10.1007/978-94-017-3552-0_6
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