Computation of dominant eigenvalues and eigenvectors : a comparative study of algorithms

We investigate two widely used recursive algorithms for the computation of eigenvectors with extreme eigenvalues of large symmetric matrices---the modified Lanczoes method and the conjugate-gradient method. The goal is to establish a connection between their underlying principles and to evaluate the...

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Bibliographic Details
Published in:Physical review. B, Condensed matter Condensed matter, 1993-09, Vol.48 (10), p.7696-7699
Main Authors: NIGHTINGALE, M. P, VISWANATH, V. S, MÜLLER, G
Format: Article
Language:English
Subjects:
661100 - Classical & Quantum Mechanics- (1992-)
665000 - Physics of Condensed Matter- (1992-)
ALGORITHMS
CALCULATION METHODS
CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSICS
CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND SUPERFLUIDITY
Condensed matter: electronic structure, electrical, magnetic, and optical properties
CONVERGENCE
EIGENVALUES
EIGENVECTORS
Electron states
Exact sciences and technology
MATHEMATICAL LOGIC
MATRICES
MECHANICS
Physics
QUANTUM MECHANICS
Theories and models of many electron systems
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Summary:We investigate two widely used recursive algorithms for the computation of eigenvectors with extreme eigenvalues of large symmetric matrices---the modified Lanczoes method and the conjugate-gradient method. The goal is to establish a connection between their underlying principles and to evaluate their performance in applications to Hamiltonian and transfer matrices of selected model systems of interest in condensed matter physics and statistical mechanics. The conjugate-gradient method is found to converge more rapidly for understandable reasons, while storage requirements are the same for both methods.
ISSN:0163-1829
1095-3795
DOI:10.1103/PhysRevB.48.7696