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Total least squares methods
Author(s) -
Markovsky Ivan,
Sima Diana M.,
Van Huffel Sabine
Publication year - 2010
Publication title -
wiley interdisciplinary reviews: computational statistics
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.693
H-Index - 38
eISSN - 1939-0068
pISSN - 1939-5108
DOI - 10.1002/wics.65
Subject(s) - regularization (linguistics) , least squares function approximation , computer science , algorithm , perturbation (astronomy) , total least squares , generalized least squares , mathematics , linear least squares , iteratively reweighted least squares , mathematical optimization , non linear least squares , statistics , estimation theory , artificial intelligence , physics , quantum mechanics , estimator , singular value decomposition
Abstract Recent advances in total least squares approaches for solving various errors‐in‐variables modeling problems are reviewed, with emphasis on the following generalizations: 1. the use of weighted norms as a measure of the data perturbation size, capturing prior knowledge about uncertainty in the data; 2. the addition of constraints on the perturbation to preserve the structure of the data matrix, motivated by structured data matrices occurring in signal and image processing, systems and control, and computer algebra; 3. the use of regularization in the problem formulation, aiming at stabilizing the solution by decreasing the effect because of intrinsic ill‐conditioning of certain problems. Copyright © 2009 John Wiley & Sons, Inc.This article is categorized under: Statistical Models > Fitting Models Algorithms and Computational Methods > Least Squares