Analysis of the generalized total least squares problem \(AX\approx B\) when some columns of \(A\) are free of error

DOI10.1007/BF01385747zbMath0803.65049OpenAlexW1995666049MaRDI QIDQ1326441

Christopher C. Paige, Musheng Wei

Publication date: 2 January 1995

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

Full work available at URL: https://eudml.org/doc/133730

zbMATH Keywords

perturbation theorygeneralized total least squares problemminimum norm correction matrices

Mathematics Subject Classification ID

Numerical solutions to overdetermined systems, pseudoinverses (65F20)

Related Items (12)

Krylov Subspace Approach to Core Problems within Multilinear Approximation Problems: A Unifying Framework ⋮ History and generality of the CS decomposition ⋮ Condition numbers of multidimensional mixed least squares-total least squares problems ⋮ An advanced algorithm for partitioning and parameter estimation in local model networks and its application to vehicle vertical dynamics ⋮ A note on the matrix-scaled total least squares problems with multiple solutions ⋮ Condition numbers of the mixed least squares-total least squares problem revisited ⋮ A Gauss-Newton method for mixed least squares-total least squares problems ⋮ Consistent estimation with the use of orthogonal projections for a linear regression model with errors in the variables ⋮ An algebraic technique for total least squares problem in quaternionic quantum theory ⋮ On perturbations of some constrained subspaces ⋮ Perturbation theory for the Eckart-Young-Mirsky theorem and the constrained total least squares problem ⋮ Perturbation analysis and condition numbers of mixed least squares-scaled total least squares problem

Uses Software

• VanHuffel

Cites Work

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• An Analysis of the Total Least Squares Problem
• A generalization of the Eckart-Young-Mirsky matrix approximation theorem
• Algebraic relationships between classical regression and total least- squares estimation
• Algebraic relations between the total least squares and least squares problems with more than one solution
• The Restricted Singular Value Decomposition of Matrix Triplets
• The Restricted Total Least Squares Problem: Formulation, Algorithm, and Properties
• Consistency of regression estimates when some variables are subject to error
• Matrix Analysis
• Computing the Generalized Singular Value Decomposition
• The Smallest Perturbation of a Submatrix that Lowers the Rank of the Matrix
• The Smallest Perturbation of a Submatrix which Lowers the Rank and Constrained Total Least Squares Problems
• Towards a Generalized Singular Value Decomposition
• The Restricted Singular Value Decomposition: Properties and Applications
• The Analysis for the Total Least Squares Problem with More Than One Solution
• Generalizing the Singular Value Decomposition
• Analysis and Properties of the Generalized Total Least Squares Problem $AX \approx B$ When Some or All Columns in A are Subject to Error

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