Algebraic connections between the least squares and total least squares problems

DOI10.1007/BF01396047zbMath0663.65038MaRDI QIDQ1114307

Joos Vandewalle, Sabine Van Huffel

Publication date: 1989

Published in: Numerische Mathematik (Search for Journal in Brave)

Full work available at URL: https://eudml.org/doc/133362

zbMATH Keywords

singular value decompositiondata fittingtotal least squaressingular vectorapproximate subspaceoverdetermined sets of linear equations

Mathematics Subject Classification ID

Numerical solutions to overdetermined systems, pseudoinverses (65F20) Eigenvalues, singular values, and eigenvectors (15A18)

Related Items (7)

About existence and uniqueness of the restricted total least squares estimation ⋮ A new error in variables model for solving positive definite linear system using orthogonal matrix decompositions ⋮ Perturbation theory for orthogonal projection methods with applications to least squares and total least squares ⋮ BACKWARD PERTURBATION ANALYSIS AND RELATIVE ALGORITHMS FOR NONSYMMETRIC LINEAR SYSTEMS WITH MULTIPLE RIGHT-HAND SIDES ⋮ Sampling minimal subsets with large spans for robust estimation ⋮ Algebraic relations between the total least squares and least squares problems with more than one solution ⋮ Perturbation analysis and condition numbers of scaled total least squares problems

Cites Work

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• An Analysis of the Total Least Squares Problem
• The influence function in the errors in variables problem
• Estimating linear statistical relationships
• Algebraic relationships between classical regression and total least- squares estimation
• Collinearity and least squares regression
• Estimation in a multivariate errors in variables regression model: Large sample results
• Estimation of a linear transformation
• Developments in Linear Regression Methodology: 1959-1982
• Consistency of regression estimates when some variables are subject to error
• Analysis and Solution of the Nongeneric Total Least Squares Problem
• A Bayesian Study of the Error-in-Variables Model
• Numerical Methods for Estimating Parameters in Nonlinear Models with Errors in the Variables
• Perturbation bounds in connection with singular value decomposition

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