Computing several eigenpairs of Hermitian problems by conjugate gradient iterations

Ovtchinnikov, E. 2008. Computing several eigenpairs of Hermitian problems by conjugate gradient iterations. Journal of Computational Physics. 227 (22), pp. 9477-9497. https://doi.org/10.1016/j.jcp.2008.06.038

TitleComputing several eigenpairs of Hermitian problems by conjugate gradient iterations
AuthorsOvtchinnikov, E.
Abstract

The paper is concerned with algorithms for computing several extreme eigenpairs of Hermitian problems based on the conjugate gradient method. We analyse computational strategies employed by various algorithms of this kind reported in the literature and identify their limitations. Our criticism is illustrated by numerical tests on a set of problems from electronic structure calculations and acoustics.

KeywordsConjugate gradient method, Eigenvalue computation
JournalJournal of Computational Physics
Journal citation227 (22), pp. 9477-9497
ISSN0021-9991
YearNov 2008
PublisherAcademic Press Professional
Digital Object Identifier (DOI)https://doi.org/10.1016/j.jcp.2008.06.038
Publication dates
PublishedNov 2008

Related outputs

Jacobi correction equation, line search, and conjugate gradients in Hermitian eigenvalue computation II: computing several extreme eigenvalues
Ovtchinnikov, E. 2008. Jacobi correction equation, line search, and conjugate gradients in Hermitian eigenvalue computation II: computing several extreme eigenvalues. SIAM Journal on Numerical Analysis. 46 (5), pp. 2593-2619. https://doi.org/10.1137/070688754

Jacobi correction equation, line search and conjugate gradients in Hermitian eigenvalue computation I: computing an extreme eigenvalue
Ovtchinnikov, E. 2008. Jacobi correction equation, line search and conjugate gradients in Hermitian eigenvalue computation I: computing an extreme eigenvalue. SIAM Journal on Numerical Analysis. 46 (5), pp. 2567-2592. https://doi.org/10.1137/070688742

Block locally optimal preconditioned eigenvalue Xolvers (BLOPEX) in Hypre and PETSc
Knyazev, A.V., Argentati, M.E., Lashuk, I. and Ovtchinnikov, E. 2007. Block locally optimal preconditioned eigenvalue Xolvers (BLOPEX) in Hypre and PETSc. SIAM Journal on Scientific Computing. 29 (5), pp. 2224-2239. https://doi.org/10.1137/060661624

Cluster robustness of preconditioned gradient subspace iteration eigensolvers
Ovtchinnikov, E. 2006. Cluster robustness of preconditioned gradient subspace iteration eigensolvers. Linear Algebra and its Applications. 415 (1), pp. 140-166. https://doi.org/10.1016/j.laa.2005.06.039

Cluster robust error estimates for the Rayleigh-Ritz approximation II: Estimates for eigenvalues
Ovtchinnikov, E. 2006. Cluster robust error estimates for the Rayleigh-Ritz approximation II: Estimates for eigenvalues. Linear Algebra and its Applications. 415 (1), pp. 188-209. https://doi.org/10.1016/j.laa.2005.06.041

Cluster robust error estimates for the Rayleigh-Ritz approximation I: Estimates for invariant subspaces
Ovtchinnikov, E. 2006. Cluster robust error estimates for the Rayleigh-Ritz approximation I: Estimates for invariant subspaces. Linear Algebra and its Applications. 415 (1), pp. 167-187. https://doi.org/10.1016/j.laa.2005.06.040

Sharp convergence estimates for the preconditioned steepest descent method for hermitian eigenvalue problems
Ovtchinnikov, E. 2006. Sharp convergence estimates for the preconditioned steepest descent method for hermitian eigenvalue problems. SIAM Journal on Numerical Analysis. 43 (6), pp. 2668-2689. https://doi.org/10.1137/040620643

Convergence estimates for the generalized davidson method for symmetric eigenvalue problems II: the subspace acceleration
Ovtchinnikov, E. 2003. Convergence estimates for the generalized davidson method for symmetric eigenvalue problems II: the subspace acceleration. SIAM Journal on Numerical Analysis. 41 (1), pp. 272-286. https://doi.org/10.1137/S0036142902411756

Convergence estimates for the generalized davidson method for symmetric eigenvalue problems I: the preconditioning aspect
Ovtchinnikov, E. 2003. Convergence estimates for the generalized davidson method for symmetric eigenvalue problems I: the preconditioning aspect. SIAM Journal on Numerical Analysis. 41 (1), pp. 258-271. https://doi.org/10.1137/S0036142902411756

On the opodeictics of successive eigenvalue relaxation for large-scale eigenvalue problems: proofs of convergence estimates
Xanthis, L. and Ovtchinnikov, E. 2002. On the opodeictics of successive eigenvalue relaxation for large-scale eigenvalue problems: proofs of convergence estimates. HERMIS: the International Journal of Computer Mathematics and its Applications. 3, pp. 65-90.

Successive eigenvalue relaxation: a new method for the generalized eigenvalue problem and convergence estimates
Ovtchinnikov, E. and Xanthis, L. 2001. Successive eigenvalue relaxation: a new method for the generalized eigenvalue problem and convergence estimates. Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences. 457 (2006), pp. 441-451. https://doi.org/10.1098/rspa.2000.0674

Permalink - https://westminsterresearch.westminster.ac.uk/item/91139/computing-several-eigenpairs-of-hermitian-problems-by-conjugate-gradient-iterations


Share this

Usage statistics

77 total views
0 total downloads
These values cover views and downloads from WestminsterResearch and are for the period from September 2nd 2018, when this repository was created.