Bruce Hendrickson and David Day, computer scientists at Sandia National Laboratories in New Mexico, recently used ARPACK with Tchebycheff polynomial preconditioning to compute the three lowest non-trivial eigenvalues and corresponding eigenvectors of a weighted Laplacian matrix of a graph. ARPACK, a software package for solving large-scale eigenvalue problems, was developed by CRPC researcher Dan Sorensen and colleagues at Rice University.
The matrix was of dimension 2.4 million, with about 44 million nonzeros. The calculation took just under 44 hours on an SGI Onyx with two R10000 processors and 3 gigabytes of RAM.
Hendrickson will use the results of the calculation in a project to visually represent the large-scale structure of scientific disciplines based upon citation analysis. This non-traditional application of eigenanalysis is representative of a growing emphasis on use of eigenanalysis in graph partitioning and data base retrieval problems.
For more information on ARPACK, including instructions on how to download the software, see http://www.caam.rice.edu/~kristyn/parpack_home.html. See the next issue of Parallel Computing Research for a "Work in Progress" article about Sorensen's current work in the area of reactive scattering codes for massively parallel architecture supercomputers.
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