Preconditioned conjugate gradient method for the sparse generalized eigenvalue problem in electronic structure calculations

DOI10.1016/S0010-4655(00)00188-0zbMath0976.65037OpenAlexW1967929760WikidataQ60264782 ScholiaQ60264782MaRDI QIDQ5934196

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Publication date: 19 December 2001

Published in: Computer Physics Communications (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/s0010-4655(00)00188-0

zbMATH Keywords

algorithmconvergencepreconditioningconjugate gradient methodgeneralized eigenvalue problemapplication to electronic structurechlorine moleculedensity functional approachlocalised basis setsilicon crystalthe first few lowest eigensolutions

Mathematics Subject Classification ID

Numerical computation of eigenvalues and eigenvectors of matrices (65F15) Dynamic continuum models (systems of particles, etc.) in time-dependent statistical mechanics (82C21) Molecular physics (81V55)

Related Items (4)

Efficacious symmetry-adapted atomic displacement method for lattice dynamical studies ⋮ Block subspace projection preconditioned conjugate gradient method in modal structural analysis ⋮ Coupling of \(h\) and \(p\) finite elements: application to free vibration analysis of plates with curvilinear plan-forms ⋮ Ab initio molecular simulations with numeric atom-centered orbitals

Cites Work

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• A new look at the Lanczos algorithm for solving symmetric systems of linear equations
• Improved algorithms for the lowest few eigenvalues and associated eigenvectors of large matrices
• The iterative calculation of a few of the lowest eigenvalues and corresponding eigenvectors of large real-symmetric matrices
• Length-scale ill conditioning in linear-scaling DFT
• A new method for diagonalising large matrices

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