Software Availability

While we have presented the IRAM as much as possible in template form, we do not recommend implementation from this description. High-quality software is freely available in the form of ARPACK. The fine detail of implementation is quite important to the robustness and ultimate success of this method. While a working method could be obtained from the description given here, it would almost certainly be deficient in some respect. One should regard this description as a detailed but still conceptual treatment.

ARPACK is a collection of FORTRAN subroutines designed to solve large scale eigenvalue problems. ARPACK stands for ARnoldi PACKage. ARPACK software is capable of solving large scale Hermitian or non-Hermitian (standard and generalized) eigenvalue problems. It has been used for a wide range of applications. Parallel ARPACK (P_ARPACK) is provided as an extension to the current ARPACK library and is targeted for distributed memory message passing systems. The message passing layers currently supported are BLACS and MPI.

The ARPACK software is based upon the IRAM that is presented in §7.6.2. When the matrix $A$ is symmetric (Hermitian) this reduces to the the implicitly restarted Lanczos method (IRLM) described in §4.5.

ARPACK provides various drivers in template form for SI. There are special drivers for banded matrices. It also provides a driver for computing a partial SVD of a general rectangular matrix. For complete information, one should consult the ARPACK Users' Guide [295].

For more information about ARPACK, including how to access it, see the book's homepage, ETHOME.