ARPACK, the ARnoldi PACKage, is a numerical
software library written in FORTRAN 77

Fortran

Fortran is a general-purpose, procedural, imperative programming language that is especially suited to numeric computation and scientific computing...

 for solving large scale eigenvalue problems.
The package is designed to compute a few eigenvalues and corresponding
eigenvectors of large sparse

Sparse matrix

In the subfield of numerical analysis, a sparse matrix is a matrix populated primarily with zeros . The term itself was coined by Harry M. Markowitz....

 or structured matrices

Matrix (mathematics)

In mathematics, a matrix is a rectangular array of numbers, symbols, or expressions. The individual items in a matrix are called its elements or entries. An example of a matrix with six elements isMatrices of the same size can be added or subtracted element by element...

, using the
Implicitly Restarted Arnoldi Method (IRAM)
or, in the case of symmetric matrices, the corresponding variant of the
Lanczos algorithm.

Reverse Communication Interface

A powerful feature of ARPACK is its ability to use any matrix storage format. This is possible because it doesn't operate on the matrices directly, but instead when a matrix operation is required it returns control to the calling program with a flag indicating what operation is required. The calling program must then perform the operation and call the ARPACK routine again to continue. The operations are typically matrix-vector products, and solving linear systems.

External links

• ARPACK homepage at Rice University