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There are a few software packages available for the Lanczos methods
described in this section. The
package, LANZ, written by Jones and Patrick [249], is
applicable to a definite pencil (5.1) with positive
semidefinite and includes SI (5.16)
and uses selective (partial)
-reorthogonalization.
The LANSO package discussed in §4.4 can also be
used for a definite pencil with SI
and selective reorthogonalization of a orthogonal basis.
The code described in [206] is a block Lanczos
algorithm with SI
that uses inertia to make sure that all eigenvalues in a
specified interval have been found. This code is currently not
in the public domain.
Implicitly restarted Lanczos method described in §4.5
is available in ARPACK [295]. ARPACK has driver routines
for the generalized Hermitian eigenproblem (5.1).
For more information about this software, including how to access
it, see the book's homepage ETHOME.
Figure 5.1:
Residual estimates, Lanczos with shift-and-invert,
L-membrane 9-point finite difference approximation.
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Next: Numerical Example.
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Susan Blackford
2000-11-20