A projected preconditioned conjugate gradient algorithm for computing many extreme eigenpairs of a Hermitian matrix

DOI10.1016/j.jcp.2015.02.030zbMath1349.65133arXiv1407.7506OpenAlexW1963825920MaRDI QIDQ349770

Eugene Vecharynski, Chao Yang, John Ernest Pask

Publication date: 5 December 2016

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

Full work available at URL: https://arxiv.org/abs/1407.7506

zbMATH Keywords

density functional theory based electronic structure calculationspreconditioned eigenvalue solvers

Mathematics Subject Classification ID

Numerical computation of eigenvalues and eigenvectors of matrices (65F15) Hermitian, skew-Hermitian, and related matrices (15B57) Preconditioners for iterative methods (65F08)

Related Items (19)

Convergence theory for preconditioned eigenvalue solvers in a nutshell ⋮ ELSI -- an open infrastructure for electronic structure solvers ⋮ On flexible block Chebyshev-Davidson method for solving symmetric generalized eigenvalue problems ⋮ A Conjugate Gradient Method for Electronic Structure Calculations ⋮ An unconditionally energy-stable and orthonormality-preserving iterative scheme for the Kohn-Sham gradient flow based model ⋮ Weighted Trace-Penalty Minimization for Full Configuration Interaction ⋮ KSSOLV 2.0: an efficient Matlab toolbox for solving the Kohn-Sham equations with plane-wave basis set ⋮ On Chebyshev-Davidson method for symmetric generalized eigenvalue problems ⋮ TRPL+K: Thick-Restart Preconditioned Lanczos+K Method for Large Symmetric Eigenvalue Problems ⋮ Gradient Flow Based Kohn--Sham Density Functional Theory Model ⋮ Gaussian basis implementation of the charge patching method ⋮ On relaxed filtered Krylov subspace method for non-symmetric eigenvalue problems ⋮ A Thick-Restart Lanczos Algorithm with Polynomial Filtering for Hermitian Eigenvalue Problems ⋮ Numerical methods for Kohn–Sham density functional theory ⋮ CoordinateWise Descent Methods for Leading Eigenvalue Problem ⋮ Fast Eigenpairs Computation with Operator Adapted Wavelets and Hierarchical Subspace Correction ⋮ Convergence Analysis of Direct Minimization and Self-Consistent Iterations ⋮ Efficient block preconditioned eigensolvers for linear response time-dependent density functional theory ⋮ Triangularized orthogonalization-free method for solving extreme eigenvalue problems

Uses Software

• ScaLAPACK
• PETSc
• BLOPEX
• ABINIT
• Quantum Espresso
• Elemental
• Qbox
• ELPA
• lobpcg.m

Cites Work

• Unnamed Item
• Unnamed Item
• The iterative calculation of a few of the lowest eigenvalues and corresponding eigenvectors of large real-symmetric matrices
• The trace minimization method for the symmetric generalized eigenvalue problem
• A spectrum slicing method for the Kohn-Sham problem
• Toward the Optimal Preconditioned Eigensolver: Locally Optimal Block Preconditioned Conjugate Gradient Method
• Numerical Methods for Large Eigenvalue Problems
• Elemental
• The Gradient Projection Method for Nonlinear Programming. Part I. Linear Constraints
• Block Locally Optimal Preconditioned Eigenvalue Xolvers (BLOPEX) in Hypre and PETSc
• Matrix Analysis
• A Simultaneous Iteration Algorithm for Real Matrices
• A Trace Minimization Algorithm for the Generalized Eigenvalue Problem
• Numerical Optimization
• ScaLAPACK Users' Guide
• Convex programming in Hilbert space
• The Gradient Projection Method for Nonlinear Programming. Part II. Nonlinear Constraints
• Some Metric Inequalities in the Space of Matrices
• Elements of structural optimization.

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