A symmetric structure-preserving {\(\Gamma\)}QR algorithm for linear response eigenvalue problems

DOI10.1016/j.laa.2017.01.005zbMath1359.65057OpenAlexW2569418226MaRDI QIDQ513231

Wen-Wei Lin, Tiexiang Li, Ren-Cang Li

Publication date: 3 March 2017

Published in: Linear Algebra and its Applications (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.laa.2017.01.005

zbMATH Keywords

numerical experimentsstructure preserving{\(\Gamma\)}QR algorithm\(\boldsymbol{\Pi}^\pm\)-matrix\(\Gamma\)-orthogonalitylinear response eigenvalue problem

Mathematics Subject Classification ID

Numerical computation of eigenvalues and eigenvectors of matrices (65F15)

Related Items

Some remarks on the complex \(J\)-symmetric eigenproblem ⋮ A projected preconditioned conjugate gradient method for the linear response eigenvalue problem ⋮ Rayleigh-Ritz majorization error bounds for the linear response eigenvalue problem ⋮ Structure-preserving \(\Gamma\) QR and \(\Gamma\)-Lanczos algorithms for Bethe-Salpeter eigenvalue problems ⋮ Thick restarting the weighted harmonic Golub-Kahan-Lanczos algorithm for the linear response eigenvalue problem

Cites Work

• Unnamed Item
• Unnamed Item
• A novel nonsymmetric \(K\)-Lanczos algorithm for the generalized nonsymmetric \(K\)-eigenvalue problems
• 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
• Eigenvalues of Ax=lambdaBx for real symmetric matrices A and B computed by reduction to a pseudosymmetric form and the HR process
• A KQZ algorithm for solving linear-response eigenvalue equations
• Convergence analysis of Lanczos-type methods for the linear response eigenvalue problem
• The periodic QR algorithm is a disguised QR algorithm
• The Multishift QR Algorithm. Part II: Aggressive Early Deflation
• Algorithm 953
• Minimization Principles for the Linear Response Eigenvalue Problem II: Computation
• Reduction of the RPA eigenvalue problem and a generalized Cholesky decomposition for real-symmetric matrices
• A Hamiltonian $QR$ Algorithm
• A symplectic QR like algorithm for the solution of the real algebraic Riccati equation
• Minimization Principles for the Linear Response Eigenvalue Problem I: Theory
• Numerical Methods for Electronic Structure Calculations of Materials

This page was built for publication: A symmetric structure-preserving {\(\Gamma\)}QR algorithm for linear response eigenvalue problems