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Weighted Total Least Squares, Rank Deficiency and Linear Matrix Structures

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

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  • Bart De Moor

    (Katholieke Universiteit Leuven, ESAT-SISTA)

Abstract

In this contribution we explain how the rank deficiency of a given data matrix, its linear matrix structure and its interpretation in terms of discrete-time dynamical systems, are intimately connected. This relation permits to formulate least squares dynamical system identification problems, the solution of which leads to structured total least squares. We also consider the insertion of given weights in the least squares objective function, leading to weighted TLS problems. The Riemannian SVD, which is a “nonlinear” generalized SVD, provides an elegant framework for these structured and/or weighted TLS problems.

Suggested Citation

  • Bart De Moor, 2002. "Weighted Total Least Squares, Rank Deficiency and Linear Matrix Structures," Springer Books, in: Sabine Van Huffel & Philippe Lemmerling (ed.), Total Least Squares and Errors-in-Variables Modeling, pages 293-304, Springer.
    • Handle: RePEc:spr:sprchp:978-94-017-3552-0_26
    DOI: 10.1007/978-94-017-3552-0_26
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