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HIGH-PERFORMANCE SOLVERS FOR DENSE HERMITIAN EIGENPROBLEMS
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DOI：10.1137/110848803.png)
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Abstract
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We introduce a new collection of solvers-subsequently called EleMRRR-for large-scale dense Hermitian eigenproblems. EleMRRR solves various types of problems: generalized, standard, and tridiagonal eigenproblems. Among these, the last is of particular importance as it is a solver in its own right, as well as the computational kernel for the first two; we present a fast and scalable tridiagonal solver based on the algorithm of multiple relatively robust representations-referred to as PMRRR. Like the other EleMRRR solvers, PMRRR is part of the freely available Elemental library, and is designed to fully support both message-passing and multithreading parallelism. As a result, the solvers are equally effective in message-passing environments with and without multithreading. We conducted a thorough performance study of EleMRRR and ScaLAPACK's solvers on two supercomputers. Such a study, performed with up to 8,192 cores, provides precise guidelines for assembling the fastest solver within the ScaLAPACK framework; it also indicates that EleMRRR outperforms even the fastest solvers built from ScaLAPACK's components.
Keywords:
generalized eigenproblem
eigenvalue
eigenvector
Hermitian
symmetric
tridiagonal
parallel algorithms
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