ARPACK is a collection of Fortran77 subroutines designed to solve large scale eigenvalue problems.
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).