NHSE Software Catalog

ARPACK

url

ftp://ftp.caam.rice.edu/pub/people/sorensen/ARPACK/

title_line

collection of Fortran 77 subroutines for solving large
scale eigenvalue problems

author

R. Lehoucq, D. Sorensen, P. Vu, C. Yang

contact

Dan Sorensen / sorensen@caam.rice.edu

abstract

The package is designed to compute a few eigenvalues and corresponding
eigenvectors of a general n by n matrix A. It is most appropriate for large
sparse or structured matrices A where structured means that a matrix-vector
product w <- Av requires order n rather than the usual order n**2
floating point operations. This software is based upon an algorithmic variant
of the Arnoldi process called the Implicitly Restarted Arnoldi Method (IRAM).
When the matrix A is symmetric it reduces to a variant of the Lanczos process
called the Implicitly Restarted Lanczos Method (IRLM). These variants
may be viewed as a synthesis of the Arnoldi/Lanczos process with the
Implicitly Shifted QR technique that is suitable for large scale problems.
For many standard problems, a matrix factorization is not required. Only
the action of the matrix on a vector is needed.

ARPACK software is capable of solving large scale symmetric, nonsymmetric,
and generalized eigenproblems from significant application areas.
The software is designed to compute a few (k) eigenvalues with user specified
features such as those of largest real part or largest magnitude.
Storage requirements are on the order of n*k locations. No auxiliary storage
is required. A set of Schur basis vectors for the desired k-dimensional
eigen-space is computed which is numerically orthogonal to working precision.
Numerically accurate eigenvectors are available on request.