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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 n2 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.
WWW: http://www.caam.rice.edu/software/ARPACK/
NOTE: You MUST link with BLAS library or a replacement like ATLAS.
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