Parallel Two-Stage Reduction to Hessenberg-Triangular Form
Copyright policy )Parallel Two-Stage Reduction to Hessenberg-Triangular Form
We present a two-stage algorithm for the parallel reduction of a pencil to Hessenberg-triangular form. Traditionally, two-stage Hessenberg-triangular reduction algorithms achieve high performance in the first stage, but struggle to achieve high performance in the second stage. Our algorithm extends techniques described by Karlsson et al. to also achieve high performance in the second stage. Experiments in a shared memory environment demonstrate that the algorithm can outperform state-of-the-art implementations.
19 pages, 11 figures
- KU Leuven Belgium
Numerical computation of eigenvalues and eigenvectors of matrices, Hessenberg-triangular, FOS: Computer and information sciences, Mathematics, Applied, Numerical & Computational Mathematics, words. generalized eigenvalues, parallel algorithm, 0102 Applied Mathematics, Hessenb erg-triangular, 4901 Applied mathematics, 65F15, 65Y05, ALGORITHM, 0802 Computation Theory and Mathematics, Science & Technology, 0103 Numerical and Computational Mathematics, generalized eigenvalues, Parallel numerical computation, Computer Science - Distributed, Parallel, and Cluster Computing, Physical Sciences, 4903 Numerical and computational mathematics, Computer Science - Mathematical Software, Distributed, Parallel, and Cluster Computing (cs.DC), Mathematical Software (cs.MS), Mathematics
Numerical computation of eigenvalues and eigenvectors of matrices, Hessenberg-triangular, FOS: Computer and information sciences, Mathematics, Applied, Numerical & Computational Mathematics, words. generalized eigenvalues, parallel algorithm, 0102 Applied Mathematics, Hessenb erg-triangular, 4901 Applied mathematics, 65F15, 65Y05, ALGORITHM, 0802 Computation Theory and Mathematics, Science & Technology, 0103 Numerical and Computational Mathematics, generalized eigenvalues, Parallel numerical computation, Computer Science - Distributed, Parallel, and Cluster Computing, Physical Sciences, 4903 Numerical and computational mathematics, Computer Science - Mathematical Software, Distributed, Parallel, and Cluster Computing (cs.DC), Mathematical Software (cs.MS), Mathematics
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