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

Tisseur, F and Dongarra, J (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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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 2010, the AMS's Mathematics Subject Classification > 65 Numerical analysis
Depositing User:	Ms Lucy van Russelt
Date Deposited:	05 Dec 2007
Last Modified:	20 Oct 2017 14:12
URI:	https://eprints.maths.manchester.ac.uk/id/eprint/981

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