Structure-preserving \(\Gamma\) QR and \(\Gamma\)-Lanczos algorithms for Bethe-Salpeter eigenvalue problems

DOI10.1016/j.cam.2018.03.010zbMath1427.65047arXiv1801.00884OpenAlexW2963585687MaRDI QIDQ2279840

Yingying Zhou, Tiexiang Li, Zhen-Chen Guo

Publication date: 16 December 2019

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

Full work available at URL: https://arxiv.org/abs/1801.00884

zbMATH Keywords

Bethe-Salpeter eigenvalue problem\(\Gamma\) QR algorithm\(\Gamma\)-Lanczos algorithm\(\Gamma\)-unitarity

Mathematics Subject Classification ID

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

Cites Work

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• A symmetric structure-preserving {\(\Gamma\)}QR algorithm for linear response eigenvalue problems
• Numerical simulation in the partial differential equation controllability analysis with physically meaningful constraints
• Structure preserving parallel algorithms for solving the Bethe-Salpeter eigenvalue problem
• Analysis of a recursive least squares hyperbolic rotation algorithm for signal processing
• An analysis of the HR algorithm for computing the eigenvalues of a matrix
• A KQZ algorithm for solving linear-response eigenvalue equations
• Fast iterative solution of the Bethe-Salpeter eigenvalue problem using low-rank and QTT tensor approximation
• Convergence analysis of Lanczos-type methods for the linear response eigenvalue problem
• Direct methods for the solution of Poisson's equation on a staggered grid
• Minimization Principles for the Linear Response Eigenvalue Problem II: Computation
• Numerical Methods for Large Eigenvalue Problems
• ON THE SPECTRAL PROPERTIES OF MATRICES ASSOCIATED WITH TREND FILTERS
• On the Rates of Convergence of the Lanczos and the Block-Lanczos Methods
• A direct Method for the Discrete Solution of Separable Elliptic Equations
• The Methods of Cyclic Reduction, Fourier Analysis and the FACR Algorithm for the Discrete Solution of Poisson’s Equation on a Rectangle
• Minimization Principles for the Linear Response Eigenvalue Problem I: Theory
• Numerical Methods for Electronic Structure Calculations of Materials
• Estimates for Some Computational Techniques in Linear Algebra

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