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). 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.
Important Features:
o Reverse Communication Interface.
o Single and Double Precision Real Arithmetic Versions for Symmetric,
Non-symmetric, Standard or Generalized Problems.
o Single and Double Precision Complex Arithmetic Versions for Standard
or Generalized Problems.
o Routines for Banded Matrices - Standard or Generalized Problems.
o Routines for The Singular Value Decomposition.
o Example driver routines that may be used as templates to implement
numerous Shift-Invert strategies for all problem types, data types
and precision.