Package Name | ARPACK / PARPACK |
Author(s) |
Rich Lehoucq ,
Kristi Maschhof,
Danny Sorensen , and Chao Yang
|
Version | 2.1 release |
Date | Sep 24, 1996 |
Language | Fortran 77, C++ wrappers available |
Platform(s) | the parallel version, PARPACK, needs MPI or BLACS |
References |
4.5
IRLM for Hermitian Eigenvalue Problem 5.5 IRLM for Generalized Hermitian Eigenvalue Problem 6.3 driver for SVD 7.6 IRAM for Non-Hermitian Eigenvalue Problem |
Functionality |
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. |
Location | http://www.caam.rice.edu/software/ARPACK/ |
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