NDLI: Parallel and Heterogeneous $m$--Hessenberg--Triangular--Triangular Reduction

Content Provider	Society for Industrial and Applied Mathematics (SIAM)
Author	Bosner, Nela Karlsson, Lars
Copyright Year	2017
Abstract	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 $2 \times 8$ CPU cores and one GPU. Future development should focus on improving the scalability of the CPU computations.
Sponsorship	Croatian Science Foundation
Starting Page	C29
Ending Page	C47
Page Count	19
File Format	PDF
ISSN	10648275
DOI	10.1137/15M1047349
e-ISSN	10957197
Issue Number	1
Volume Number	39
Language	English
Publisher	Society for Industrial and Applied Mathematics
Publisher Date	2017-01-12
Access Restriction	Subscribed
Subject Keyword	solving shifted linear systems Computational methods Canonical forms, reductions, classification Complexity and performance of numerical algorithms Direct methods for linear systems and matrix inversion Transformations Linear equations Canonical structure Givens rotations heterogeneous CPU/GPU implementation Parallel algorithms $m$-Hessenberg--triangular--triangular form
Content Type	Text
Resource Type	Article
Subject	Applied Mathematics Computational Mathematics

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