A harmonic Lanczos bidiagonalization method for computing interior singular triplets of large matrices

DOI10.1016/j.amc.2012.01.013zbMath1246.65065arXiv1001.3258OpenAlexW1973321137MaRDI QIDQ433291

Datian Niu, Xue-Gang Yuan

Publication date: 13 July 2012

Published in: Applied Mathematics and Computation (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1001.3258

zbMATH Keywords

algorithmsingular value decompositionnumerical experimentsharmonic Lanczos bidiagonalization methodharmonic shiftsimplicit restarting techniqueLanczos bidiagonalization processRayleigh quotient matrixsingular triplets

Mathematics Subject Classification ID

Numerical solutions to overdetermined systems, pseudoinverses (65F20)

Related Items (5)

An implicitly restarted block Lanczos bidiagonalization method using Leja shifts ⋮ Computing the smallest singular triplets of a large matrix ⋮ Thick restarting the weighted harmonic Golub-Kahan-Lanczos algorithm for the linear response eigenvalue problem ⋮ On computing the minimum singular value of a tensor sum ⋮ On Inner Iterations of Jacobi--Davidson Type Methods for Large SVD Computations

Uses Software

• eigs
• PROPACK
• IRAM
• na26

Cites Work

• Unnamed Item
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• A Refined Harmonic Lanczos Bidiagonalization Method and an Implicitly Restarted Algorithm for Computing the Smallest Singular Triplets of Large Matrices
• A Block Lanczos Method for Computing the Singular Values and Corresponding Singular Vectors of a Matrix
• Implicit Application of Polynomial Filters in a k-Step Arnoldi Method
• An Implicitly Restarted Refined Bidiagonalization Lanczos Method for Computing a Partial Singular Value Decomposition
• Implicitly Restarted GMRES and Arnoldi Methods for Nonsymmetric Systems of Equations
• Low-Rank Matrix Approximation Using the Lanczos Bidiagonalization Process with Applications
• The convergence of harmonic Ritz values, harmonic Ritz vectors and refined harmonic Ritz vectors
• Augmented Implicitly Restarted Lanczos Bidiagonalization Methods

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