Computer Physics Communications Program LibraryPrograms in Physics & Physical Chemistry |

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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_0Distribution 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. | ||

Restrictions: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. |

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