In this paper, an e ective scheme is given, which can solve eigenvalue for large sparse matrixes based on spectrum division method. In this scheme, we divide the spectrum into several intervals and extract eigenvalues from each subinterval independently. To estimate the eigenvalue distribution, the Gerschgorin Circle Theorem is used. In addition, an inter- polation method, aimed to find the subintervals, is applied to reduce calculation amount. In this paper, a multistage parallel algorithm, combined with spectral projection method and approximate spectral projection method based on contour integral, is given. The validity, balance, and e ciency of this algorithm are veried in supercomputer "shenteng7000" and "yuan". Working on 1024 processors, the performance of this parallel algorithm improves five times compared with the general algorithm.
MUItifrontal Massively Parallel Sparse direct Solver, http://www.mumos.enseeiht.fr/, 1999-2011.
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