ACM Transactions on Mathematical Software (TOMS)
A parallel/recursive algorithm
Journal of Computational Physics
A parallel symmetric block-tridiagonal divide-and-conquer algorithm
ACM Transactions on Mathematical Software (TOMS)
Resolution of large symmetric eigenproblems on a world-wide grid
International Journal of Grid and Utility Computing
A new algorithm for singular value decomposition and its parallelization
Parallel Computing
ACM Transactions on Mathematical Software (TOMS)
MR3-SMP: A symmetric tridiagonal eigensolver for multi-core architectures
Parallel Computing
Parallelization of divide-and-conquer eigenvector accumulation
Euro-Par'05 Proceedings of the 11th international Euro-Par conference on Parallel Processing
Divide and Conquer on Hybrid GPU-Accelerated Multicore Systems
SIAM Journal on Scientific Computing
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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 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.