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A parallel divide and conquer algorithm for the symmetric eigenvalue problem on distributed memory architectures
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DOI：10.1137/S1064827598336951.png)
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Abstract
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We present a new parallel implementation of a divide and conquer algorithm for computing the spectral decomposition of a symmetric tridiagonal matrix on distributed memory architectures. The implementation we develop differs from other implementations in that we use a two-dimensional block cyclic distribution of the data, we use the Lowner theorem approach to compute orthogonal eigenvectors, and we introduce permutations before the back transformation of each rank-one update in order to make good use of deflation. This algorithm yields the first scalable, portable, and numerically stable parallel divide and conquer eigensolver. Numerical results confirm the effectiveness of our algorithm. We compare performance of the algorithm with that of the QR algorithm and of bisection followed by inverse iteration on an IBM SP2 and a cluster of Pentium PIIs.
Keywords:
divide and conquer
symmetric eigenvalue problem
tridiagonal matrix
rank-one modification
parallel algorithm
ScaLAPACK
LAPACK
distributed memory architecture
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