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PARALLEL AND HETEROGENEOUS m-HESSENBERG-TRIANGULAR-TRIANGULAR REDUCTION
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DOI：10.1137/15M1047349.png)
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Abstract
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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.
Keywords:
m-Hessenberg-triangular-triangular form
solving shifted linear systems
Givens rotations
heterogeneous CPU/GPU implementation
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