Band Generalization of the Golub--Kahan Bidiagonalization, Generalized Jacobi Matrices, and the Core Problem

DOI10.1137/140968914zbMath1320.65057OpenAlexW2095124951MaRDI QIDQ5254384

Zdeněk Strakoš, Iveta Hnetynkova, Martin Plešinger

Publication date: 9 June 2015

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

Full work available at URL: https://semanticscholar.org/paper/f5ad76df4c456078cd614c458e16835ceb5f013a

zbMATH Keywords

multiple right-hand sidesGolub-Kahan bidiagonalizationcore problemgeneralized Jacobi matricestotal least squares 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 (10)

Krylov Subspace Approach to Core Problems within Multilinear Approximation Problems: A Unifying Framework ⋮ 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 ⋮ Complex wedge-shaped matrices: a generalization of Jacobi matrices ⋮ Total least squares problem with the arbitrary unitarily invariant norms ⋮ On TLS formulation and core reduction for data fitting with generalized models ⋮ Randomized core reduction for discrete ill-posed problem ⋮ Solvability classes for core problems in matrix total least squares minimization. ⋮ Band Generalization of the Golub--Kahan Bidiagonalization, Generalized Jacobi Matrices, and the Core Problem ⋮ A Block Bidiagonalization Method for Fixed-Accuracy Low-Rank Matrix Approximation

Uses Software

• VanHuffel
• symrcm
• OPQ

Cites Work

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• An Analysis of the Total Least Squares Problem
• Lanczos tridiagonalization and core problems
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• Reorthogonalization for the Golub-Kahan-Lanczos bidiagonal reduction
• 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
• Calculating the Singular Values and Pseudo-Inverse of a Matrix

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