Projective block Lanczos algorithm for dense, Hermitian eigensystems
Journal Article
·
· Journal of Computational Physics
- State Univ. of New York, Stony Brook, NY (United States)
Projection operators are used to effect {open_quotes}deflation by restriction{close_quotes} and it is argued that this is an optimal Lanczos algorithm for memory minimization. Algorithmic optimization is constrained to dense, Hermitian eigensystems where a significant number of the extreme eigenvectors must be obtained reliably and completely. The defining constraints are operator algebra without a matrix representation and semi-orthogonalization without storage of Krylov vectors. other semi-orthogonalization strategies for Lanczos algorithms and conjugate gradient techniques are evaluated within these constraints. Large scale, sparse, complex numerical experiments are performed on clusters of magnetic dipoles, a quantum many-body system that is not block-diagonalizable. Plane-wave, density functional theory of beryllium clusters provides examples of dense complex eigensystems. Use of preconditioners and spectral transformations is evaluated in a preprocessor prior to a high accuracy self-consistent field calculation. 25 refs., 3 figs., 5 tabs.
- OSTI ID:
- 274230
- Journal Information:
- Journal of Computational Physics, Journal Name: Journal of Computational Physics Journal Issue: 1 Vol. 124; ISSN 0021-9991; ISSN JCTPAH
- Country of Publication:
- United States
- Language:
- English
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