Linear response eigenvalue problem solved by extended locally optimal preconditioned conjugate gradient methods

DOI10.1007/s11425-016-0297-1zbMath1358.65021OpenAlexW2410795307MaRDI QIDQ341304

WenWei Lin, Ren-Cang Li, Zhaojun Bai

Publication date: 16 November 2016

Published in: Science China. Mathematics (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/s11425-016-0297-1

zbMATH Keywords

algorithmnumerical exampleeigenvalue problempreconditioningdeflationlinear responseconjugate-gradient

Mathematics Subject Classification ID

Numerical computation of eigenvalues and eigenvectors of matrices (65F15) Direct numerical methods for linear systems and matrix inversion (65F05)

Related Items (10)

Heavy ball restarted CMRH methods for linear systems ⋮ Eigenvalue inclusion sets for linear response eigenvalue problems ⋮ On generalizing trace minimization principles. II ⋮ Numerical methods for Bogoliubov-de Gennes excitations of Bose-Einstein condensates ⋮ Efficient and accurate algorithms for solving the Bethe-Salpeter eigenvalue problem for crystalline systems ⋮ A block Lanczos method for the linear response eigenvalue problem ⋮ Error bounds for approximate deflating subspaces for linear response eigenvalue problems ⋮ Preconditioned gradient iterations for the eigenproblem of definite matrix pairs ⋮ Trace minimization method via penalty for linear response eigenvalue problems ⋮ On generalizing trace minimization principles

Uses Software

• EIGIFP
• LAPACK
• Quantum Espresso
• lobpcg.m

Cites Work

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• An adaptive block Lanczos algorithm
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• Minimization principles and computation for the generalized linear response eigenvalue problem
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• Minimization Principles for the Linear Response Eigenvalue Problem II: Computation
• Extensions of Wielandt’s min–max principles for positive semi-definite pencils
• Vibrational states of nuclei in the random phase approximation
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• On the Rates of Convergence of the Lanczos and the Block-Lanczos Methods
• An Inverse Free Preconditioned Krylov Subspace Method for Symmetric Generalized Eigenvalue Problems
• Minimization Principles for the Linear Response Eigenvalue Problem I: Theory
• Accuracy of the $s$-Step Lanczos Method for the Symmetric Eigenproblem in Finite Precision
• Algorithm 845
• Error bounds of Rayleigh-Ritz type contour integral-based eigensolver for solving generalized eigenvalue problems

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