A parallel Davidson-type algorithm for several eigenvalues

DOI10.1006/jcph.1998.6003zbMath0948.65035OpenAlexW1968344387MaRDI QIDQ1287171

Suely Oliveira, Leonardo S. Borges

Publication date: 13 November 2000

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

Full work available at URL: https://semanticscholar.org/paper/1d8e04af2abcbe515ef1c2f8b0ebf988b5dd119d

zbMATH Keywords

eigenvaluesparallel algorithmsDavidson methodarrowhead matrices

Mathematics Subject Classification ID

Computational methods for sparse matrices (65F50) Numerical computation of eigenvalues and eigenvectors of matrices (65F15) Parallel numerical computation (65Y05)

Related Items (4)

LEFTMOST EIGENVALUE OF REAL AND COMPLEX SPARSE MATRICES ON PARALLEL COMPUTER USING APPROXIMATE INVERSE PRECONDITIONING ⋮ A Rayleigh-Chebyshev procedure for finding the smallest eigenvalues and associated eigenvectors of large sparse Hermitian matrices ⋮ New methods for calculations of the lowest eigenvalues of the real symmetric generalized eigenvalue problem ⋮ ANALYSIS OF DIFFERENT PARTITIONING SCHEMES FOR PARALLEL GRAM-SCHMIDT ALGORITHMS

Uses Software

• LAPACK
• BLAS
• EISPACK
• ARPACK
• MPI
• BRENT
• DVDSON

Cites Work

• Parallel QR factorization by Householder and modified Gram-Schmidt algorithms
• Computing the eigenvalues and eigenvectors of symmetric arrowhead matrices
• A parallel alternating direction implicit preconditioning method
• A new look at the Lanczos algorithm for solving symmetric systems of linear equations
• Improved algorithms for the lowest few eigenvalues and associated eigenvectors of large matrices
• The iterative calculation of a few of the lowest eigenvalues and corresponding eigenvectors of large real-symmetric matrices
• Matrix eigensystem routines - EISPACK guide. 2nd ed
• Super-matrix methods
• An implicit restarted Lanczos method for large symmetric eigenvalue problems
• A Davidson program for finding a few selected extreme eigenpairs of a large, sparse, real, symmetric matrix
• Note on the Parallel Efficiency of the Frederickson-McBryan Multigrid Algorithm
• A Parallel Version of a Multigrid Algorithm for Isotropic Transport Equations
• A set of level 3 basic linear algebra subprograms
• A new parallel chasing algorithm for transforming arrowhead matrices to tridiagonal form
• Normalized Convergence Rates for the PSMG Method
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item

This page was built for publication: A parallel Davidson-type algorithm for several eigenvalues