Resolution of large symmetric eigenproblems on a world-wide grid
International Journal of Grid and Utility Computing
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The homotopy method has been used in the past for finding zeros of nonlinear functions. Early algorithms based on the homotopy approach for solving the symmetric eigenproblem suffer either from insufficient orthogonality between computed eigenvectors or from low efficiency. A new algorithm presented in this article overcomes these problems by using deflation of close eigenpairs and maintains a high degree of parallelism by applying the divide-and-conquer principle. A numerical comparison of a sequential implementation of the new algorithm shows that it is competitive with other well-established algorithms both in speed and accuracy. Algorithms based on the homotopy method are excellent candidates for multicomputers because of their natural parallelism. This article examines how the algorithm can be implemented on distributed-memory multicomputers. The experimental performance results obtained on an Intel Paragon multicomputer are very satisfying.