Weighted Golub-Kahan-Lanczos bidiagonalization algorithms

zbMath1392.65101MaRDI QIDQ1744310

Hong-Xiu Zhong Hongguo Xu

Publication date: 23 April 2018

Published in: ETNA. Electronic Transactions on Numerical Analysis (Search for Journal in Brave)

Full work available at URL: http://etna.mcs.kent.edu/volumes/2011-2020/vol47/abstract.php?vol=47&pages=153-178

zbMATH Keywords

eigenvalueeigenvectorbidiagonal matricesKrylov subspaceRitz vectorlinear response eigenvalue problemRitz valueweighted Golub-Kahan-Lanczos bidiagonalization algorithm

Mathematics Subject Classification ID

Numerical computation of eigenvalues and eigenvectors of matrices (65F15) Eigenvalues, singular values, and eigenvectors (15A18)

Related Items (4)

Eigenvalue inclusion sets for linear response eigenvalue problems ⋮ Rayleigh-Ritz majorization error bounds for the linear response eigenvalue problem ⋮ Thick restarting the weighted harmonic Golub-Kahan-Lanczos algorithm for the linear response eigenvalue problem ⋮ Trace minimization method via penalty for linear response eigenvalue problems

Uses Software

• LSQR
• SparseMatrix

Cites Work

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• Convergence analysis of Lanczos-type methods for the linear response eigenvalue problem
• Minimization Principles for the Linear Response Eigenvalue Problem II: Computation
• Generalized Golub--Kahan Bidiagonalization and Stopping Criteria
• The university of Florida sparse matrix collection
• Numerical Methods for Large Eigenvalue Problems
• LSQR: An Algorithm for Sparse Linear Equations and Sparse Least Squares
• Solving Generalized Least-Squares Problems with LSQR
• Minimization Principles for the Linear Response Eigenvalue Problem I: Theory
• Calculating the Singular Values and Pseudo-Inverse of a Matrix
• Bidiagonalization of Matrices and Solution of Linear Equations

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