New distributed-memory parallel algorithms for solving nonsymmetric eigenvalue problems
- Univ. of Guelph, Ontario (Canada)
In this article we present new distributed-memory parallel algorithms for finding all eigenvalues of a general real matrix using Hessenberg reduction and implicit double-shift QR iterations. The parallel algorithm for Hessenberg reduction employs a two-dimensional {gamma}1 x {gamma}2 subcube-grid network. A two-dimensional data wrap-mapping scheme and the subcube-doubling communication technique are adopted. The advantages are: the communication volume can be minimized by appropriate choices of {gamma}1 and {gamma}2; furthermore, the lengths of the messages exchanged during the row transformation and the column transformation are decreasing as {gamma}1 and {gamma}2 increase, respectively. The second parallel algorithm finds the complete set of eigenvalues of an upper Hessenberg matrix by QR iterations. It uses a novel dynamic block-diagonal wrap-mapping scheme to allocate data to the processors on a ring communication network, which facilitates temporary data relocation to match the data access pattern in each double-shift QR iteration. The proposed dynamic data mapping/relocation strategy improves the workload balancing and reduces the processor idle time. This enhancement is shown to be effective in solving large-scale problems.
- OSTI ID:
- 125574
- Report Number(s):
- CONF-950212--; CNN: Grant OGP0121352
- Country of Publication:
- United States
- Language:
- English
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