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Parallel and Heterogeneous $m$-Hessenberg-Triangular-Triangular Reduction
Umeå University, Faculty of Science and Technology, Department of Computing Science.
2017 (English)In: SIAM Journal on Scientific Computing, ISSN 1064-8275, E-ISSN 1095-7197, Vol. 39, no 1, C29-C47 p.Article in journal (Refereed) Published
Abstract [en]

The m-Hessenberg-triangular-triangular (mHTT) reduction is a simultaneous orthogonal reduction of three matrices to condensed form. It has applications, for example, in solving shifted linear systems arising in various control theory problems. A new heterogeneous CPU/GPU implementation of the mHTT reduction is presented and evaluated against an existing CPU implementation. The algorithm offloads the compute-intensive matrix-matrix multiplications to the GPU and keeps the inner loop, which is memory intensive and has a complicated control flow, on the CPU. Experiments demonstrate that the heterogeneous implementation can be superior to the existing CPU implementation on a system with 2 x 8 CPU cores and one GPU. Future development should focus on improving the scalability of the CPU computations.

Place, publisher, year, edition, pages
2017. Vol. 39, no 1, C29-C47 p.
Keyword [en]
m-Hessenberg-triangular-triangular form, solving shifted linear systems, Givens rotations, terogeneous CPU/GPU implementation
National Category
Control Engineering
Identifiers
URN: urn:nbn:se:umu:diva-133267DOI: 10.1137/15M1047349ISI: 000395747800025OAI: oai:DiVA.org:umu-133267DiVA: diva2:1087475
Available from: 2017-04-07 Created: 2017-04-07 Last updated: 2017-04-07Bibliographically approved

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Karlsson, Lars
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