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A Parallel Algorithm for Computing the Extremal Eigenvalues of Very Large
Sparse Matrices.

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Abstract

Quantum mechanics often give rise to problems where one needs to find a
few eigenvalues of very large sparse matrices. The size of the matrices
is such that it is not possible to store them in main memory but instead
they must be generated on the fly. In this paper the method of coordinate
relaxation is applied to one class of such problems. A parallel algorithm
based on graph coloring is proposed. Experimental results on a Cray Origin
2000 computer show that the algorithm converges fast ant that it also scales
well as more processors are applied. Comparisons show that the convergence
of the presented algorithm is much faster on the given test problems than
using ARPACK \cite{LSV96}.

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