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arXiv · 2301.07964

Parallel two-stage reduction to Hessenberg-triangular form

Thijs Steel·Raf Vandebril
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Abstract

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.

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Thijs Steel, Raf Vandebril. 2023-01-19. Parallel two-stage reduction to Hessenberg-triangular form. https://arxiv.org/abs/2301.07964

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