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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.
...and more!
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