Structured total least squares and L2 approximation problems
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In this article, it is shown how structured and weighted total least squares and L 2 approximation problems lead to a nonlinear generalized singular value decomposition, and an inverse iteration scheme to find a (local) minimum is proposed.About:
This article is published in Linear Algebra and its Applications.The article was published on 1993-07-01 and is currently open access. It has received 153 citations till now. The article focuses on the topics: Total least squares & Non-linear least squares.read more
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Ministry of Education and Science of the Russian Federation
TL;DR: The abstract should follow the structure of the article (relevance, degree of exploration of the problem, the goal, the main results, conclusion) and characterize the theoretical and practical significance of the study results.
Journal ArticleDOI
Robust Solutions to Least-Squares Problems with Uncertain Data
Laurent El Ghaoui,Hervé Lebret +1 more
TL;DR: This work considers least-squares problems where the coefficient matrices A,b are unknown but bounded and minimize the worst-case residual error using (convex) second-order cone programming, yielding an algorithm with complexity similar to one singular value decomposition of A.
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Overview of total least-squares methods
Ivan Markovsky,Sabine Van Huffel +1 more
TL;DR: It is explained how special structure of the weight matrix and the data matrix can be exploited for efficient cost function and first derivative computation that allows to obtain computationally efficient solution methods.
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Survey paper: Structured low-rank approximation and its applications
TL;DR: This work outlines applications in system theory (approximate realization, model reduction, output error, and errors-in-variables identification), signal processing, signal processing (harmonic retrieval, sum-of-damped exponentials, and finite impulse response modeling), and computer algebra (Approximate common divisor).
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Total least squares for affinely structured matrices and the noisy realization problem
TL;DR: It is shown with some simple counter examples that "classical" algorithms such as the Steiglitz-McBride (1965), iterative quadratic maximum likelihood and Cadzow's (1988) iteration do not converge to the optimal L/sub 2/ solution, despite misleading claims in the literature.
References
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LIII. On lines and planes of closest fit to systems of points in space
TL;DR: This paper is concerned with the construction of planes of closest fit to systems of points in space and the relationships between these planes and the planes themselves.
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The approximation of one matrix by another of lower rank
Carl Eckart,Gale Young +1 more
TL;DR: In this paper, the problem of approximating one matrix by another of lower rank is formulated as a least-squares problem, and the normal equations cannot be immediately written down, since the elements of the approximate matrix are not independent of one another.
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N4SID: subspace algorithms for the identification of combined deterministic-stochastic systems
TL;DR: Two new N4SID algorithms to identify mixed deterministic-stochastic systems are derived and these new algorithms are compared with existing subspace algorithms in theory and in practice.
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An Analysis of the Total Least Squares Problem
Gene H. Golub,Charles Van Loan +1 more
TL;DR: In this article, a singular value decomposition analysis of the TLS problem is presented, which provides a measure of the underlying problem's sensitivity and its relationship to ordinary least squares regression.