Algebraic relations between the total least squares and least squares problems with more than one solution

DOI10.1007/BF01396223zbMath0761.65030OpenAlexW2088028136MaRDI QIDQ1203413

Musheng Wei

Publication date: 8 February 1993

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

Full work available at URL: https://eudml.org/doc/133645

zbMATH Keywords

singular value decompositionoverdetermined systemtotal least squaresperturbation boundalgebraic relationrank deficientweighted squared residuals

Mathematics Subject Classification ID

Numerical solutions to overdetermined systems, pseudoinverses (65F20) Theory of matrix inversion and generalized inverses (15A09) Eigenvalues, singular values, and eigenvectors (15A18) Linear equations (linear algebraic aspects) (15A06)

Related Items (21)

Analysis of the generalized total least squares problem \(AX\approx B\) when some columns of \(A\) are free of error ⋮ On a basic multivariate EIV model with linear equality constraints ⋮ Krylov Subspace Approach to Core Problems within Multilinear Approximation Problems: A Unifying Framework ⋮ On condition numbers of the total least squares problem with linear equality constraint ⋮ History and generality of the CS decomposition ⋮ Condition numbers of multidimensional mixed least squares-total least squares problems ⋮ Solvability of the Core Problem with Multiple Right-Hand Sides in the TLS Sense ⋮ TLS formulation and core reduction for problems with structured right-hand sides ⋮ Perturbation theory for orthogonal projection methods with applications to least squares and total least squares ⋮ Higher Order Extended Dynamic Mode Decomposition Based on the Structured Total Least Squares ⋮ Condition numbers of the multidimensional total least squares problems having more than one solution ⋮ Condition Numbers of the Multidimensional Total Least Squares Problem ⋮ An algebraic technique for total least squares problem in quaternionic quantum theory ⋮ A note on the scaled total least squares problem ⋮ On TLS formulation and core reduction for data fitting with generalized models ⋮ The original tls solution sets of the multidimensional TLS problem^∗ ⋮ Perturbation theory for the Eckart-Young-Mirsky theorem and the constrained total least squares problem ⋮ Solvability classes for core problems in matrix total least squares minimization. ⋮ Extension of the total least square problem using general unitarily invariant norms ⋮ Band Generalization of the Golub--Kahan Bidiagonalization, Generalized Jacobi Matrices, and the Core Problem ⋮ Multidimensional Total Least Squares Problem with Linear Equality Constraints

Cites Work

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• An Analysis of the Total Least Squares Problem
• Perturbation of the least squares problem
• Algebraic relationships between classical regression and total least- squares estimation
• The partial total least squares algorithm
• Algebraic connections between the least squares and total least squares problems
• A Note on a Result of Sun Ji-Guang: Sensitivity of the CS and GSV Decompositions
• Analysis and Solution of the Nongeneric Total Least Squares Problem
• Towards a Generalized Singular Value Decomposition
• The Analysis for the Total Least Squares Problem with More Than One Solution
• On the Perturbation of Pseudo-Inverses, Projections and Linear Least Squares Problems
• Computation of exponentials in transient data

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