Basis selection in LOBPCG

DOI10.1016/j.jcp.2006.02.007zbMath1104.65031OpenAlexW2040436854MaRDI QIDQ853191

Richard B. Lehoucq, Ulrich Hetmaniuk

Publication date: 15 November 2006

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

Full work available at URL: https://doi.org/10.1016/j.jcp.2006.02.007

zbMATH Keywords

numerical examplespreconditioningconjugate gradient methodorthonormalizationLOBPCGpreconditioned eigensolversymmetric generalized eigenvalue problem

Mathematics Subject Classification ID

Numerical computation of eigenvalues and eigenvectors of matrices (65F15) Numerical computation of matrix norms, conditioning, scaling (65F35)

Related Items (16)

Linear response eigenvalue problem solved by extended locally optimal preconditioned conjugate gradient methods ⋮ Multiscale modal analysis of fully-loaded spent nuclear fuel canisters ⋮ Hybrid eigensolvers for nuclear configuration interaction calculations ⋮ On flexible block Chebyshev-Davidson method for solving symmetric generalized eigenvalue problems ⋮ An indefinite variant of LOBPCG for definite matrix pencils ⋮ Hierarchical subspace evolution method for super large parallel computing: A linear solver and an eigensolver as examples ⋮ Householder Orthogonalization with a Nonstandard Inner Product ⋮ A mixed precision LOBPCG algorithm ⋮ Modified-operator method for the calculation of band diagrams of crystalline materials ⋮ Randomized Projection for Rank-Revealing Matrix Factorizations and Low-Rank Approximations ⋮ Low-rank Riemannian eigensolver for high-dimensional Hamiltonians ⋮ Computing several eigenpairs of Hermitian problems by conjugate gradient iterations ⋮ JADAMILU: a software code for computing selected eigenvalues of large sparse symmetric matrices ⋮ A Robust and Efficient Implementation of LOBPCG ⋮ Preconditioned gradient iterations for the eigenproblem of definite matrix pairs ⋮ Efficient block preconditioned eigensolvers for linear response time-dependent density functional theory

Uses Software

• LAPACK
• Matlab
• BLAS
• Trilinos
• lobpcg.m

Cites Work

• Unnamed Item
• Efficient solution of symmetric eigenvalue problems using multigrid preconditioners in the locally optimal block conjugate gradient method
• Algebraic multigrid by smoothed aggregation for second and fourth order elliptic problems
• Toward the Optimal Preconditioned Eigensolver: Locally Optimal Block Preconditioned Conjugate Gradient Method
• Analysis of the Cholesky Method with Iterative Refinement for Solving the Symmetric Definite Generalized Eigenproblem
• An overview of the Trilinos project
• Block Locally Optimal Preconditioned Eigenvalue Xolvers (BLOPEX) in Hypre and PETSc
• LAPACK Users' Guide
• A set of level 3 basic linear algebra subprograms
• An Efficient and Stable Algorithm for the Symmetric-Definite Generalized Eigenvalue Problem
• A Block Orthogonalization Procedure with Constant Synchronization Requirements
• A comparison of eigensolvers for large-scale 3D modal analysis using AMG-preconditioned iterative methods

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