A Refined Harmonic Lanczos Bidiagonalization Method and an Implicitly Restarted Algorithm for Computing the Smallest Singular Triplets of Large Matrices

DOI10.1137/080733383zbMath1215.65072arXiv0906.2242OpenAlexW2065931256MaRDI QIDQ3084401

Publication date: 16 March 2011

Published in: SIAM Journal on Scientific Computing (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/0906.2242

zbMATH Keywords

algorithm numerical examples singular values singular vectors implicit restart large scale problems Lanczos bidiagonalization numerical comparison singular triplets harmonic shift refined projection

Mathematics Subject Classification ID

Numerical computation of eigenvalues and eigenvectors of matrices (65F15) Numerical solutions to overdetermined systems, pseudoinverses (65F20)

Related Items (22)

On the computation of a truncated SVD of a large linear discrete ill-posed problem ⋮ The Joint Bidiagonalization Method for Large GSVD Computations in Finite Precision ⋮ A Preconditioned Hybrid SVD Method for Accurately Computing Singular Triplets of Large Matrices ⋮ Majorization bounds for SVD ⋮ An implicitly restarted block Lanczos bidiagonalization method using Leja shifts ⋮ Mixed and componentwise condition numbers for a linear function of the solution of the total least squares problem ⋮ On the condition number of the total least squares problem ⋮ An augmented LSQR method ⋮ The Convergence of Harmonic Ritz Vectors and Harmonic Ritz Values, Revisited ⋮ Two harmonic Jacobi-Davidson methods for computing a partial generalized singular value decomposition of a large matrix pair ⋮ A FEAST SVDsolver based on Chebyshev-Jackson series for computing partial singular triplets of large matrices ⋮ Hybrid iterative refined restarted Lanczos bidiagonalization methods ⋮ Harmonic multi-symplectic Lanczos algorithm for quaternion singular triplets ⋮ Explicit deflation in Golub-Kahan-Lanczos bidiagonalization methods ⋮ A harmonic Lanczos bidiagonalization method for computing interior singular triplets of large matrices ⋮ Computing the smallest singular triplets of a large matrix ⋮ On choices of formulations of computing the generalized singular value decomposition of a large matrix pair ⋮ An implicitly restarted Lanczos bidiagonalization method with refined harmonic shifts for computing smallest singular triplets ⋮ PRIMME_SVDS: A High-Performance Preconditioned SVD Solver for Accurate Large-Scale Computations ⋮ On computing the minimum singular value of a tensor sum ⋮ Approximation accuracy of the Krylov subspaces for linear discrete ill-posed problems ⋮ On Inner Iterations of Jacobi--Davidson Type Methods for Large SVD Computations

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