35 lines
2.1 KiB
Text
35 lines
2.1 KiB
Text
ARPACK is a collection of Fortran77 subroutines designed to solve large
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scale eigenvalue problems.
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The package is designed to compute a few eigenvalues and corresponding
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eigenvectors of a general n by n matrix A. It is most appropriate for large
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sparse or structured matrices A where structured means that a matrix-vector
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product w <- Av requires order n rather than the usual order n**2 floating
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point operations. This software is based upon an algorithmic variant of the
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Arnoldi process called the Implicitly Restarted Arnoldi Method (IRAM). When
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the matrix A is symmetric it reduces to a variant of the Lanczos process
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called the Implicitly Restarted Lanczos Method (IRLM). These variants may be
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viewed as a synthesis of the Arnoldi/Lanczos process with the Implicitly
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Shifted QR technique that is suitable for large scale problems. For many
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standard problems, a matrix factorization is not required. Only the action
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of the matrix on a vector is needed. ARPACK software is capable of solving
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large scale symmetric, nonsymmetric, and generalized eigenproblems from
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significant application areas. The software is designed to compute a few (k)
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eigenvalues with user specified features such as those of largest real part
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or largest magnitude. Storage requirements are on the order of n*k locations.
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No auxiliary storage is required. A set of Schur basis vectors for the desired
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k-dimensional eigen-space is computed which is numerically orthogonal to working
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precision. Numerically accurate eigenvectors are available on request.
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Important Features:
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o Reverse Communication Interface.
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o Single and Double Precision Real Arithmetic Versions for Symmetric,
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Non-symmetric, Standard or Generalized Problems.
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o Single and Double Precision Complex Arithmetic Versions for Standard
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or Generalized Problems.
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o Routines for Banded Matrices - Standard or Generalized Problems.
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o Routines for The Singular Value Decomposition.
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o Example driver routines that may be used as templates to implement
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numerous Shift-Invert strategies for all problem types, data types
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and precision.
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