Weighted Total Least Squares, Rank Deficiency and Linear Matrix Structures

Bart De Moor ()
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Bart De Moor: Katholieke Universiteit Leuven, ESAT-SISTA

A chapter in Total Least Squares and Errors-in-Variables Modeling, 2002, pp 293-304 from Springer

Abstract: 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.

Keywords: dynamic errors-in-variables; elementwise weighted total least squares; Hankel TLS; Riemannian SVD; system identification. (search for similar items in EconPapers)
Date: 2002
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Persistent link: https://EconPapers.repec.org/RePEc:spr:sprchp:978-94-017-3552-0_26

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DOI: 10.1007/978-94-017-3552-0_26

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