On TLS formulation and core reduction for data fitting with generalized models

DOI10.1016/j.laa.2019.04.018zbMath1420.65053OpenAlexW2936163611MaRDI QIDQ2002685

Jana Žáková, Martin Plešinger, Iveta Hnetynkova

Publication date: 12 July 2019

Published in: Linear Algebra and its Applications (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.laa.2019.04.018

zbMATH Keywords

core problemmultiple observationsorthogonal regressionerror-in-variables modelingtotal least squares problem (TLS)tensor approximation problem

Mathematics Subject Classification ID

Numerical solutions to overdetermined systems, pseudoinverses (65F20) Theory of matrix inversion and generalized inverses (15A09) Multilinear algebra, tensor calculus (15A69) Canonical forms, reductions, classification (15A21) Orthogonalization in numerical linear algebra (65F25)

Related Items (1)

Krylov Subspace Approach to Core Problems within Multilinear Approximation Problems: A Unifying Framework

Uses Software

• VanHuffel
• Algorithm 862

Cites Work

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• Tensor Decompositions and Applications
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• Monotonicity of unitarily invariant norms
• Consistent estimation in the bilinear multivariate errors-in-variables model
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• Scaled total least squares fundamentals
• TLS formulation and core reduction for problems with structured right-hand sides
• Solvability classes for core problems in matrix total least squares minimization.
• The Core Problem within a Linear Approximation Problem $AX\approx B$ with Multiple Right-Hand Sides
• Total least squares problem with the arbitrary unitarily invariant norms
• The Total Least Squares Problem in AX≈B: A New Classification with the Relationship to the Classical Works
• Solvability of the Core Problem with Multiple Right-Hand Sides in the TLS Sense
• Extension of the total least square problem using general unitarily invariant norms
• Algorithm 862
• The Analysis for the Total Least Squares Problem with More Than One Solution
• On solution of total least squares problems with multiple right‐hand sides
• The original tls solution sets of the multidimensional TLS problem^∗
• Band Generalization of the Golub--Kahan Bidiagonalization, Generalized Jacobi Matrices, and the Core Problem
• Core Problems in Linear Algebraic Systems

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