A block Chebyshev-Davidson method for linear response eigenvalue problems

DOI10.1007/s10444-016-9455-2zbMath1357.65046OpenAlexW2316170522MaRDI QIDQ503482

Yunkai Zhou, Ren-Cang Li, Zhongming Teng

Publication date: 12 January 2017

Published in: Advances in Computational Mathematics (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/s10444-016-9455-2

zbMATH Keywords

numerical exampleeigenvalueeigenvectorconvergence rateRitz valuesChebyshev polynomiallinear responseDavidson-type methodupper bound estimator

Mathematics Subject Classification ID

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

Related Items (8)

A distributed block Chebyshev-Davidson algorithm for parallel spectral clustering ⋮ A projected preconditioned conjugate gradient method for the linear response eigenvalue problem ⋮ A block Lanczos method for the linear response eigenvalue problem ⋮ Rayleigh-Ritz majorization error bounds for the linear response eigenvalue problem ⋮ Error bounds for approximate deflating subspaces for linear response eigenvalue problems ⋮ Backward perturbation analysis and residual-based error bounds for the linear response eigenvalue problem ⋮ Thick restarting the weighted harmonic Golub-Kahan-Lanczos algorithm for the linear response eigenvalue problem ⋮ Trace minimization method via penalty for linear response eigenvalue problems

Uses Software

• TRLan
• SparseMatrix
• Quantum Espresso
• ClusterES
• a-TRLan
• CheFSI

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Bounding the spectrum of large Hermitian matrices
• A block Chebyshev-Davidson method with inner-outer restart for large eigenvalue problems
• Chebyshev-filtered subspace iteration method free of sparse diagonalization for solving the Kohn-Sham equation
• A spectral scheme for Kohn-Sham density functional theory of clusters
• Backward perturbation analysis and residual-based error bounds for the linear response eigenvalue problem
• Self-consistent-field calculations using Chebyshev-filtered subspace iteration
• A sharp version of Kahan's theorem on clustered eigenvalues
• Convergence analysis of Lanczos-type methods for the linear response eigenvalue problem
• On the convergence rate of a preconditioned subspace eigensolver
• A Rayleigh-Chebyshev procedure for finding the smallest eigenvalues and associated eigenvectors of large sparse Hermitian matrices
• Matrix Algorithms
• 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
• Adaptive Projection Subspace Dimension for the Thick-Restart Lanczos Method
• The university of Florida sparse matrix collection
• Vibrational states of nuclei in the random phase approximation
• A Chebyshev–Davidson Algorithm for Large Symmetric Eigenproblems
• Canonical formulation of a generalized coupled dispersionless system
• Convergence Estimates for the Generalized Davidson Method for Symmetric Eigenvalue Problems I: The Preconditioning Aspect
• Convergence Estimates for the Generalized Davidson Method for Symmetric Eigenvalue Problems II: The Subspace Acceleration
• GMRES with Deflated Restarting
• Minimization Principles for the Linear Response Eigenvalue Problem I: Theory

This page was built for publication: A block Chebyshev-Davidson method for linear response eigenvalue problems