High-performance implementation of Chebyshev filter diagonalization for interior eigenvalue computations

DOI10.1016/j.jcp.2016.08.027zbMath1376.65055arXiv1510.04895OpenAlexW2211971732MaRDI QIDQ1685101

Bruno Lang, Andreas Alvermann, Andreas Pieper, Gerhard Wellein, Martin Galgon, Holger Fehske, Georg Hager, Moritz Kreutzer

Publication date: 13 December 2017

Published in: Journal of Computational Physics (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1510.04895

zbMATH Keywords

quantum physicsinterior eigenvaluesChebyshev filter polynomialsperformance engineeringtopological materials

Mathematics Subject Classification ID

Computational methods for sparse matrices (65F50) Numerical computation of eigenvalues and eigenvectors of matrices (65F15) Performance evaluation, queueing, and scheduling in the context of computer systems (68M20) Quantum dots as quasi particles (81V65)

Related Items (3)

Limited‐memory polynomial methods for large‐scale matrix functions ⋮ Solving large-scale interior eigenvalue problems to investigate the vibrational properties of the boson peak regime in amorphous materials ⋮ Benefits from using mixed precision computations in the ELPA-AEO and ESSEX-II eigensolver projects

Uses Software

• PARDISO
• FEAST
• ARPACK
• ILUPACK
• likwid
• CIRR

Cites Work

• Adaptive procedure for estimating parameters for the nonsymmetric Tchebychev iteration
• Computing interior eigenvalues of large matrices
• Self-consistent-field calculations using Chebyshev-filtered subspace iteration
• The Tchebychev iteration for nonsymmetric linear systems
• A projection method for generalized eigenvalue problems using numerical integration.
• Kernel polynomial approximations for densities of states and spectral functions
• Dissecting the FEAST algorithm for generalized eigenproblems
• CIRR: a Rayleigh-Ritz method with contour integral for generalized eigenvalue problems
• Communication-optimal Parallel and Sequential QR and LU Factorizations
• Exact diagonalization of quantum-spin models
• Efficient estimation of eigenvalue counts in an interval
• Numerical Methods for Large Eigenvalue Problems
• The kernel polynomial method
• Chebyshev Acceleration Techniques for Solving Nonsymmetric Eigenvalue Problems
• Numerical methods for large eigenvalue problems
• Increasing the Performance of the Jacobi--Davidson Method by Blocking
• Perturbation Bounds for Matrix Eigenvalues
• ARPACK Users' Guide
• A Block Orthogonalization Procedure with Constant Synchronization Requirements
• Approximate solutions and eigenvalue bounds from Krylov subspaces
• On Large-Scale Diagonalization Techniques for the Anderson Model of Localization

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