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Manuscript Title: POWEV: a subroutine package to evaluate eigenvalues and eigenvectors of large sparse matrices.
Authors: S.J. Sciutto
Program title: POWEV
Catalogue identifier: ACNR_v1_0
Distribution format: gz
Journal reference: Comput. Phys. Commun. 77(1993)95
Programming language: Fortran.
Computer: MICROVAX II.
Operating system: VMS V4.7.
RAM: 255K words
Word size: 32
Keywords: General purpose, Matrix, Eigenvalues, Eigenvectors, Power method, Chebyshev iterations, Compact storage, Discrete systems.
Classification: 4.8.

Subprograms used:
Cat Id Title Reference
ACNQ_v1_0 SPARSEM CPC 77(1993)84

Nature of problem:
The numeric eigenvalue problem appears in a number of branches of Physics. Problems such as resolution of discrete systems with many degrees of freedom, exact diagonalization of quantum clusters, etc., require the calculation of eigenvalues and eigenvectors of large sparse matrices.

Solution method:
The eigenvalues and eigenvectors are obtained using the well-known power method [3], in a new implementation which combines it with Chebyshev iterations and automatic parameter setting [4]. The routines were designed to be used with large real symmetric sparse matrices written in compact format [2]. Nonetheless, they can be applied also to non symmetric real matrices [4], and the code can be easily modified for use with complex hermitian sparse matrices.

Matrix sizes are only limited by the amount of memory available on the computer. Iterations may fail to converge when the matrix possesses two or more nearly equal eigenvalues.

Running time:
97 seconds for the test run.

[1] For language definition, see "Programming in VAX FORTRAN," Digital Equipment Corporation publication AA-D034D-TE; Maynard (MA), U.S.A. (1984).
[2] S.J. Sciutto, Universidad Nacional de La Plata, preprint (1992), submitted to Comp. Phys. Commun.
[3] J.H. Wilkinson, "The Algebraic Eigenvalue Problem," Oxford University Press, London (1977).
[4] S.J. Sciutto, Universidad Nacional de la Plata, preprint (1991).