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Recent Developments in Rank Revealing and Lanczos Methods for TLS-Related Problems

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

Author

Listed:
  • Ricardo D. Fierro

    (California State University, Department of Mathematics)

  • Per Christian Hansen

    (Technical University of Denmark, Informatics and Mathematical Modelling Building 321)

Abstract

The singular value decomposition (SVD) of a data matrix is useful for providing rank and subspace information as well as solving and analyzing total least squares (TLS) problems. Rank-revealing decompositions, herein referred to as UTV decompositions, and Lanczos methods have been proposed as substitutes for the SVD in various applications through the years. These type of methods are appropriate for solving TLS-related problems because they can efficiently and reliably provide an orthogonal basis that accurately approximates the needed numerical row space or null space. The development and availability of reliable and robust codes for TLS algorithms always lags the pace of the literature. We discuss some recent developments in the use of UTV decompositions and Lanczos methods for solving TLS-related problems along with related Matlab codes.

Suggested Citation

  • Ricardo D. Fierro & Per Christian Hansen, 2002. "Recent Developments in Rank Revealing and Lanczos Methods for TLS-Related Problems," Springer Books, in: Sabine Van Huffel & Philippe Lemmerling (ed.), Total Least Squares and Errors-in-Variables Modeling, pages 47-56, Springer.
    • Handle: RePEc:spr:sprchp:978-94-017-3552-0_5
    DOI: 10.1007/978-94-017-3552-0_5
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