27 lines
1.5 KiB
Plaintext
27 lines
1.5 KiB
Plaintext
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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
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large sparse or structured matrices A where structured means that a
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matrix-vector product w <- Av requires order n rather than the usual
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order n2 floating point operations. This software is based upon an
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algorithmic variant of the Arnoldi process called the Implicitly
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Restarted Arnoldi Method (IRAM). When the matrix A is symmetric it
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reduces to a variant of the Lanczos process called the Implicitly
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Restarted Lanczos Method (IRLM). These variants may be viewed as a
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synthesis of the Arnoldi/Lanczos process with the Implicitly Shifted QR
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technique that is suitable for large scale problems. For many standard
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problems, a matrix factorization is not required. Only the action of the
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matrix on a vector is needed.
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ARPACK software is capable of solving large scale symmetric,
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nonsymmetric, and generalized eigenproblems from significant application
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areas. The software is designed to compute a few (k) eigenvalues with
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user specified features such as those of largest real part or largest
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magnitude. Storage requirements are on the order of n*k locations. No
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auxiliary storage is required. A set of Schur basis vectors for the
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desired k-dimensional eigen-space is computed which is numerically
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orthogonal to working precision. Numerically accurate eigenvectors are
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available on request.
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