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Manuscript Title: A vectorizable eigenvalue solver for sparse matrices.
Authors: L.C. Bernard, F.J. Helton
Program title: EIGVEC
Catalogue identifier: AARI_v1_0
Distribution format: gz
Journal reference: Comput. Phys. Commun. 25(1982)73
Programming language: Fortran, CAL Assembler.
Computer: CRAY-1.
Operating system: LTSS.
RAM: 22K words
Word size: 64
Peripherals: disc.
Keywords: General purpose, Matrix, Numerical mathematics, Eigenvalue problem, Inverse vector iteration, Block matrix, Symmetric matrix, Sparse matrix, Pattern recognition, Vectorization.
Classification: 4.8.

Nature of problem:
This package solves the generalized eigenvalue problem Ax = lambdaBx, a problem which arises often, for example, in: physics, mechanics, and chemistry. Here A and B have a global block diagonal form and fine sparse structure as found in two-dimensional problems with a finite element approach.

Solution method:
Any mode can be obatined by first shifting the spectrum, then using inverse vector iteration to converge toward the lowest eigenvalue in absolute value. The Cholesky decomposition of A is efficiently done using vectorization. Sparse matrix techniques reduce I/O requirements and improve the Cholesky decomposition in some cases.

Both matrices, A and B, must be real symmetric, and B must be positive- definite. Both must have the same sparsity pattern.

Unusual features:
The program uses two subroutines written in assembly language for vectorization. The nonstandard FORTR AN statement, NAMELIST, is used.