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The structured total least‐squares approach for non‐linearly structured matrices
Author(s) -
Lemmerling P.,
Van Huffel S.,
De Moor B.
Publication year - 2002
Publication title -
numerical linear algebra with applications
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.02
H-Index - 53
eISSN - 1099-1506
pISSN - 1070-5325
DOI - 10.1002/nla.276
Subject(s) - mathematics , singular value decomposition , total least squares , vandermonde matrix , least squares function approximation , singular value , non linear least squares , generalized least squares , estimator , linear least squares , extension (predicate logic) , matrix (chemical analysis) , mathematical optimization , algorithm , statistics , computer science , physics , eigenvalues and eigenvectors , quantum mechanics , programming language , materials science , composite material
In this paper, an extension of the structured total least‐squares (STLS) approach for non‐linearly structured matrices is presented in the so‐called ‘Riemannian singular value decomposition’ (RiSVD) framework. It is shown that this type of STLS problem can be solved by solving a set of Riemannian SVD equations. For small perturbations the problem can be reformulated into finding the smallest singular value and the corresponding right singular vector of this Riemannian SVD. A heuristic algorithm is proposed. Some examples of Vandermonde‐type matrices are used to demonstrate the improved accuracy of the obtained parameter estimator when compared to other methods such as least squares (LS) or total least squares (TLS). Copyright © 2002 John Wiley & Sons, Ltd.