Solvability of the Core Problem with Multiple Right-Hand Sides in the TLS Sense

DOI10.1137/15M1028339zbMath1343.15002OpenAlexW2494638940MaRDI QIDQ3185671

Iveta Hnetynkova, Diana Maria Sima, Martin Plešinger

Publication date: 4 August 2016

Published in: SIAM Journal on Matrix Analysis and Applications (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1137/15m1028339

zbMATH Keywords

multiple right-hand sidescore problemorthogonal regressionlinear approximation problemerror-in-variables modelingclassical TLS algorithmtotal least squares (TLS) problem

Mathematics Subject Classification ID

Numerical solutions to overdetermined systems, pseudoinverses (65F20) Matrix equations and identities (15A24) Eigenvalues, singular values, and eigenvectors (15A18) Linear equations (linear algebraic aspects) (15A06) Canonical forms, reductions, classification (15A21) Orthogonalization in numerical linear algebra (65F25)

Related Items (8)

Krylov Subspace Approach to Core Problems within Multilinear Approximation Problems: A Unifying Framework ⋮ Condition numbers of multidimensional mixed least squares-total least squares problems ⋮ TLS formulation and core reduction for problems with structured right-hand sides ⋮ On TLS formulation and core reduction for data fitting with generalized models ⋮ Least squares solutions to the rank-constrained matrix approximation problem in the Frobenius norm ⋮ Randomized core reduction for discrete ill-posed problem ⋮ Solvability classes for core problems in matrix total least squares minimization. ⋮ Multidimensional Total Least Squares Problem with Linear Equality Constraints

Uses Software

• VanHuffel

Cites Work

• Unnamed Item
• An Analysis of the Total Least Squares Problem
• The extended classical total least squares algorithm
• Algebraic relations between the total least squares and least squares problems with more than one solution
• The Core Problem within a Linear Approximation Problem $AX\approx B$ with Multiple Right-Hand Sides
• The Total Least Squares Problem in AX≈B: A New Classification with the Relationship to the Classical Works
• The Analysis for the Total Least Squares Problem with More Than One Solution
• Band Generalization of the Golub--Kahan Bidiagonalization, Generalized Jacobi Matrices, and the Core Problem
• Core Problems in Linear Algebraic Systems

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