کد مقاله | کد نشریه | سال انتشار | مقاله انگلیسی | نسخه تمام متن |
---|---|---|---|---|
524185 | 868566 | 2011 | 12 صفحه PDF | دانلود رایگان |
We describe a hybrid Lyapunov solver based on the matrix sign function, where the intensive parts of the computation are accelerated using a graphics processor (GPU) while executing the remaining operations on a general-purpose multi-core processor (CPU). The initial stage of the iteration operates in single-precision arithmetic, returning a low-rank factor of an approximate solution. As the main computation in this stage consists of explicit matrix inversions, we propose a hybrid implementation of Gauß–Jordan elimination using look-ahead to overlap computations on GPU and CPU. To improve the approximate solution, we introduce an iterative refinement procedure that allows to cheaply recover full double-precision accuracy. In contrast to earlier approaches to iterative refinement for Lyapunov equations, this approach retains the low-rank factorization structure of the approximate solution. The combination of the two stages results in a mixed-precision algorithm, that exploits the capabilities of both general-purpose CPUs and many-core GPUs and overlaps critical computations. Numerical experiments using real-world data and a platform equipped with two Intel Xeon QuadCore processors and an Nvidia Tesla C1060 show a significant efficiency gain of the hybrid method compared to a classical CPU implementation.
Research highlights
► An original mixed-precision technique for the solution of Lyapunov equations is introduced.
► A high performance implementation for the solution of Lyapunov equations on a hybrid CPU-GPU architecture is described.
► The paper shows how the computation of a matrix inverse can be notoriously accelerated using a GPU and Gauss-Jordan elimination.
Journal: Parallel Computing - Volume 37, Issue 8, August 2011, Pages 439–450