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2007.225: A Parallel Divide and Conquer Algorithm for the Symmetric Eigenvalue Problem on Distributed Memory Architectures

2007.225: F Tisseur and J Dongarra (1999) A Parallel Divide and Conquer Algorithm for the Symmetric Eigenvalue Problem on Distributed Memory Architectures. SIAM Journal on Scientific Computing, 20 (6). pp. 2223-2236. ISSN 1095-7197

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DOI: 10.1137/S1064827598336951

Abstract

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 Löwner 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.

Item Type:Article
Uncontrolled Keywords:divide and conquer; symmetric eigenvalue problem; tridiagonal matrix; rank-one modification; parallel algorithm; ScaLAPACK; LAPACK; distributed memory architecture
Subjects:MSC 2000 > 65 Numerical analysis
MIMS number:2007.225
Deposited By:Ms Helen Kirkbright
Deposited On:05 December 2007

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