Algorithm 807: The SBR Toolbox—software for successive band reduction
ACM Transactions on Mathematical Software (TOMS)
An implementation of parallel eigenvalue computation using dual-level hybrid parallelism
ICA3PP'07 Proceedings of the 7th international conference on Algorithms and architectures for parallel processing
Elemental: A New Framework for Distributed Memory Dense Matrix Computations
ACM Transactions on Mathematical Software (TOMS)
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We describe a parallel algorithm for finding the eigenvalues and eigenvectors of a dense symmetric matrix, with an emphasis on the dense linear algebra operations. We follow the traditional three-step process: reduce to tridiagonal form, solve the tridiagonal problem, then backtransform the result. Since the different steps have different algorithmic characteristics, this problem serves as a perfect vehicle for exploring some issues associated with parallel linear algebra calculations. In particular, we examine the effects of matrix distribution and blocking on the computational performance of tridiagonalization and backtransformation. Through experiments on an Intel Paragon, we demonstrate that block storage of the matrix is not necessary for a highly efficient block algorithm. The performance of our approach compares very favorably with that of the corresponding ScaLAPACK routines.