A parallel divide and conquer algorithm for the symmetric eigenvalue problem on distributed memory architectures
The authors 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 they develop differs from other implementations in that they use a two-dimensional block cyclic distribution of the data, they use the Loewner theorem approach to compute orthogonal eigenvectors, and they 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 the algorithm. They 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.
- Research Organization:
- Univ. of Manchester (GB)
- Sponsoring Organization:
- US Department of Energy
- OSTI ID:
- 20005552
- Journal Information:
- SIAM Journal on Scientific Computing, Journal Name: SIAM Journal on Scientific Computing Journal Issue: 6 Vol. 20; ISSN 1064-8275; ISSN SJOCE3
- Country of Publication:
- United States
- Language:
- English
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