/netlib/lanz

======== index for lanz =======

LANZ: Software for Solving the Large Sparse Symmetric Generalized Eigenproblem
Mark T. Jones, Argonne National Laboratory, Argonne, Illinois 60439-4844
Merrell L. Patrick, Duke University, Durham, North Carolina 27706
LANZ solves the symmetric generalized eigenproblem,
\begin{equation}
Kx=\lambda Mx,
\end{equation}
where $K$ is symmetric positive definite and $M$ is
positive semi-definite. It is also capable of solving
\begin{equation}
Kx=-\lambda Mx,
\end{equation}
where $M$ can be indefinite.
It can find either 1) all
the eigenpairs in a user-specified range, or 2) the $p$ eigenpairs
closest to some user-specified value, $\sigma$.
The LANZ package was developed to run efficiently on a range of
architectures, including vector and parallel computers.
LANZ is an implementation of the algorithm described in
\cite{jones:lanczos}. The heart of LANZ is
the Lanczos algorithm used with spectral transformations
similar to those described in \cite{nour-omid:implement}. LANZ uses
the partial reorthogonalization algorithm, originally proposed
in \cite{simon:partial}, and expanded upon in \cite{parlett:semi_ortho},
to maintain semi-orthogonality among the Lanczos vectors.
In addition, LANZ uses a dynamic shifting algorithm to accelerate
convergence to desired eigenpairs in a slightly different fashion
than in \cite{boeing:small_lan_report}.
\bibitem{jones:lanczos}
{\sc Jones, M.~T., and Patrick, M.~L.}
\newblock {The Use of Lanczos's Method to Solve the Large Generalized
Symmetric Definite Eigenvalue Problem}.
\newblock Technical Report 89-67, Institute for Computer Applications in
Science and Engineering (ICASE), NASA Langley Research Center, Hampton, VA,
1989.
\bibitem{nour-omid:implement}
{\sc Nour-Omid, B., Parlett, B.~N., Ericsson, T., and Jensen, P.~S.}
\newblock {How to Implement the Spectral Transformation}.
\newblock {\em Mathematics of Computation 48}, 178 (April 1987), 663--673.
\bibitem{simon:partial}
{\sc Simon, H.~D.}
\newblock {The Lanczos Algorithm With Partial Reorthogonalization}.
\newblock {\em Mathematics of Computation 42}, 165 (January 1984), 115--142.
\bibitem{parlett:semi_ortho}
{\sc Parlett, B.~N., Nour-Omid, B., and Liu, Z.~A.}
\newblock {How to Maintain Semi-Orthogonality Among Lanczos Vectors}.
\newblock {PAM-420}, Center for Pure and Applied Mathematics, University of
California, Berkeley, July, 1988.
\bibitem{boeing:small_lan_report}
{\sc Grimes, R.~G., Lewis, J.~G., and Simon, H.~D.}
\newblock {The Implementation of a Block Lanczos Algorithm with
Reorthogonalization Methods}.
\newblock {ETA-TR-91}, Boeing Computer Servies, Seattle, WA, May, 1988.

• file: lanz/lanz_file1.tgz
  for: code, documentation, makefiles, etc.
  size: 51 kilobytes
• file: lanz/lanz_file2.tgz
  for: code, documentation, makefiles, etc.
  size: 169 kilobytes
• file: lanz/lanz_file3
  for: just code, no documentation
  size: 464 kilobytes
  lang: Fortran
• file: lanz/lanz_file4
  size: 4 kilobytes
  lang: C

  Installation of LANZ, depending on your architecture, may take up
  to 3.5mb of disk space. After installing LANZ, if you desire, you
  can delete all but one or two files created by the installation
  process.
  

• index help

Eric and Jack

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