An a posteriori verification method for generalized real-symmetric eigenvalue problems in large-scale electronic state calculations

DOI10.1016/j.cam.2020.112830zbMath1439.65046arXiv1904.06461OpenAlexW3006729389MaRDI QIDQ1987430

Katsuhisa Ozaki, Takeo Hoshi, Takeshi Ogita, Takeshi Terao

Publication date: 15 April 2020

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

Full work available at URL: https://arxiv.org/abs/1904.06461

zbMATH Keywords

verification methodsupercomputerwave functionfundamental Schrödinger-type equationsgeneralized real-symmetric eigenvalue problem, electronic state calculationlarge scale calculation

Mathematics Subject Classification ID

Numerical computation of eigenvalues and eigenvectors of matrices (65F15) Schrödinger operator, Schrödinger equation (35J10) Spectral and related methods applied to problems in solid mechanics (74S25) Specification and verification (program logics, model checking, etc.) (68Q60) Applications to the sciences (65Z05) Algorithms with automatic result verification (65G20) Mathematical aspects of software engineering (specification, verification, metrics, requirements, etc.) (68N30)

Related Items (3)

Generalized eigenvalue problem for interval matrices ⋮ Verified eigenvalue and eigenvector computations using complex moments and the Rayleigh-Ritz procedure for generalized Hermitian eigenvalue problems ⋮ Unnamed Item

Uses Software

• C-XSC
• C-XSC 2.0
• ScaLAPACK
• INTLAB
• ELPA
• GitHub
• EigenKernel
• EigenExa
• ELSES
• k-ep

Cites Work

• Unnamed Item
• Unnamed Item
• Ab initio molecular simulations with numeric atom-centered orbitals
• Numerical enclosure for each eigenvalue in generalized eigenvalue problem
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• Iterative refinement for symmetric eigenvalue decomposition. II. Clustered eigenvalues
• Numerical aspect of large-scale electronic state calculation for flexible device material
• Benefits from using mixed precision computations in the ELPA-AEO and ESSEX-II eigensolver projects
• EigenKernel
• Solution of the \(k\)-th eigenvalue problem in large-scale electronic structure calculations
• Error bounds for approximate solutions of systems of equations
• Rigorous Error Bounds for Computer Eigensystems
• ScaLAPACK Users' Guide
• Electronic Structure
• A simple method for error bounds of eigenvalues of symmetric matrices

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