Lanczos tridiagonalization and core problems

DOI10.1016/j.laa.2006.05.006zbMath1111.65041OpenAlexW2058280509MaRDI QIDQ869895

Zdeněk Strakoš, Iveta Hnetynkova

Publication date: 9 March 2007

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

Full work available at URL: https://doi.org/10.1016/j.laa.2006.05.006

zbMATH Keywords

algorithmsJacobi matrixorthogonal transformationGolub-Kahan bidiagonalizationcore problemLanczos tridiagonalizationlinear approximation problem

Mathematics Subject Classification ID

Iterative numerical methods for linear systems (65F10) Orthogonalization in numerical linear algebra (65F25)

Related Items

MINRES: From Negative Curvature Detection to Monotonicity Properties, The regularizing effect of the Golub-Kahan iterative bidiagonalization and revealing the noise level in the data, Complex wedge-shaped matrices: a generalization of Jacobi matrices, Two projection methods for regularized total least squares approximation, Extended Lanczos bidiagonalization algorithm for low rank approximation and its applications, Perturbation analysis and condition numbers of scaled total least squares problems, Band Generalization of the Golub--Kahan Bidiagonalization, Generalized Jacobi Matrices, and the Core Problem

Uses Software

• LSQR
• CRAIG

Cites Work

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• A bidiagonalization algorithm for solving large and sparse ill-posed systems of linear equations
• An implicit shift bidiagonalization algorithm for ill-posed systems
• Scaled total least squares fundamentals
• Estimation of the \(L\)-curve via Lanczos bidiagonalization
• LSQR: An Algorithm for Sparse Linear Equations and Sparse Least Squares
• Core Problems in Linear Algebraic Systems
• Calculating the Singular Values and Pseudo-Inverse of a Matrix
• Bidiagonalization of Matrices and Solution of Linear Equations