A Structure Preserving Lanczos Algorithm for Computing the Optical Absorption Spectrum

DOI10.1137/16M1102641zbMath1391.65089arXiv1611.02348WikidataQ129921234 ScholiaQ129921234MaRDI QIDQ4643326

Chao Yang, Steven G. Louie, Lin Lin, MeiYue Shao, Jack Deslippe, Felipe H. Da Jornada

Publication date: 24 May 2018

Published in: SIAM Journal on Matrix Analysis and Applications (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1611.02348

zbMATH Keywords

Gauss quadratureBethe-Salpeter equationmatrix functionalstructure preserving algorithmTamm-Dancoff approximationoptical absorption spectrumLanczos procedure

Mathematics Subject Classification ID

Numerical computation of eigenvalues and eigenvectors of matrices (65F15) Numerical computation of matrix exponential and similar matrix functions (65F60)

Related Items (6)

A note on ``Perturbation bounds for Williamson's symplectic normal form ⋮ Computing the density of states for optical spectra of molecules by low-rank and QTT tensor approximation ⋮ Efficient and accurate algorithms for solving the Bethe-Salpeter eigenvalue problem for crystalline systems ⋮ The Lanczos Algorithm Under Few Iterations: Concentration and Location of the Output ⋮ Rayleigh-Ritz majorization error bounds for the linear response eigenvalue problem ⋮ Fast optical absorption spectra calculations for periodic solid state systems

Uses Software

• BerkeleyGW
• BSEPACK
• TurboEELS

Cites Work

• Generalized averaged Gauss quadrature rules for the approximation of matrix functionals
• TurboEELS -- a code for the simulation of the electron energy loss and inelastic X-ray scattering spectra using the Liouville-Lanczos approach to time-dependent density-functional perturbation theory
• Structure preserving parallel algorithms for solving the Bethe-Salpeter eigenvalue problem
• An implicitly restarted symplectic Lanczos method for the Hamiltonian eigenvalue problem
• Some remarks on the complex \(J\)-symmetric eigenproblem
• Fast iterative solution of the Bethe-Salpeter eigenvalue problem using low-rank and QTT tensor approximation
• On Hamiltonian and symplectic Lanczos processes
• \texttt{turboTDDFT} -- a code for the simulation of molecular spectra using the Liouville-Lanczos approach to time-dependent density-functional perturbation theory
• Convergence analysis of Lanczos-type methods for the linear response eigenvalue problem
• Efficient block preconditioned eigensolvers for linear response time-dependent density functional theory
• Minimization Principles for the Linear Response Eigenvalue Problem II: Computation
• On generalized averaged Gaussian formulas
• Non-Adiabatic Meson Theory of Nuclear Forces
• A Relativistic Equation for Bound-State Problems
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