Software Availability.

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 $B$ positive semidefinite and includes SI (5.16) and uses selective (partial) $B$-reorthogonalization. The LANSO package discussed in §4.4 can also be used for a definite pencil with SI and selective reorthogonalization of a $B$ 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.