The algebraic eigenvalue problem
The algebraic eigenvalue problem
What have we learnt from using real parallel machines to solve real problems?
C3P Proceedings of the third conference on Hypercube concurrent computers and applications - Volume 2
Solving the algebraic Riccati equation on a hypercube multiprocessor
C3P Proceedings of the third conference on Hypercube concurrent computers and applications - Volume 2
A Novel Parallel QR Algorithm for Hybrid Distributed Memory HPC Systems
SIAM Journal on Scientific Computing
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Distributed-memory algorithms for finding the eigenvalues and eigenvectors of a dense unsymmetric matrix are given. While several parallel algorithms have been developed for symmetric systems, little work has been done on the unsymmetric case. Our parallel implementation proceeds in three major steps: reduction of the original matrix to Hessenberg form, application of the implicit double-shift QR algorithm to compute the eigenvalues, and back transformations to compute the eigenvectors. Several modifications to our parallel QR algorithm, including ring communication and pipelining, are discussed and compared. Results and timings are given.