Multitasking the Davidson algorithm for the large, sparse eigenvalue problem

Journal Article · Sun Jan 01 00:00:00 EST 1989 · International Journal of Supercomputer Application; (USA)

DOI:https://doi.org/10.1177/109434208900300404· OSTI ID:7128959

Umar, V M; Fischer, C F ^[1]

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1. Vanderbilt Univ., Nashville, TN (USA)

The authors report how the Davidson algorithm, developed for handling the eigenvalue problem for large and sparse matrices arising in quantum chemistry, was modified for use in atomic structure calculations. To date these calculations have used traditional eigenvalue methods, which limit the range of feasible calculations because of their excessive memory requirements and unsatisfactory performance attributed to time-consuming and costly processing of zero valued elements. The replacement of a traditional matrix eigenvalue method by the Davidson algorithm reduced these limitations. Significant speedup was found, which varied with the size of the underlying problem and its sparsity. Furthermore, the range of matrix sizes that can be manipulated efficiently was expended by more than one order or magnitude. On the CRAY X-MP the code was vectorized and the importance of gather/scatter analyzed. A parallelized version of the algorithm obtained an additional 35% reduction in execution time. Speedup due to vectorization and concurrency was also measured on the Alliant FX/8.

• OSTI ID: 7128959
• Journal Information: International Journal of Supercomputer Application; (USA), Vol. 3:4; ISSN 0890-2720
• Country of Publication: United States
• Language: English

Related Subjects

99 GENERAL AND MISCELLANEOUS//MATHEMATICS, COMPUTING, AND INFORMATION SCIENCE
74 ATOMIC AND MOLECULAR PHYSICS
ATOMS
ELECTRONIC STRUCTURE
CRAY COMPUTERS
VECTOR PROCESSING
ALGORITHMS
COMPUTER CALCULATIONS
EIGENVALUES
PARALLEL PROCESSING
COMPUTERS
MATHEMATICAL LOGIC
PROGRAMMING
990200* - Mathematics & Computers
640302 - Atomic
Molecular & Chemical Physics- Atomic & Molecular Properties & Theory