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# ======== 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_file1.tgz for code, documentation, makefiles, etc. size 51 kilobytes file lanz_file2.tgz for code, documentation, makefiles, etc. size 169 kilobytes file lanz_file3 for just code, no documentation size 464 kilobytes lang Fortran file 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.