Name
Title | ||
|---|---|---|
A mixed-precision algorithm for the solution of Lyapunov equations on hybrid CPU-GPU platforms |
Abstract | ||
|---|---|---|
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 Gausz-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. |
Year | DOI | Venue |
|---|---|---|
2011 | 10.1016/j.parco.2010.12.002 | Parallel Computing |
Keywords | Field | DocType |
explicit matrix inversion,lyapunov equations,hybrid implementation,lyapunov equation,mixed-precision algorithm,hybrid lyapunov solver,hybrid method,intel xeon quadcore processor,general-purpose cpus,approximate solution,model reduction,graphics processors,multi-core processors,iterative refinement,classical cpu implementation,hybrid cpu-gpu platform,general-purpose multi-core processor,matrix sign function,look ahead,multi core processor,multi core processors | Iterative refinement,Lyapunov function,Matrix (mathematics),Computer science,CUDA,Parallel computing,Algorithm,Theoretical computer science,Xeon,Solver,Multi-core processor,Computation | Journal |
Volume | Issue | ISSN |
37 | 8 | Parallel Computing |
Citations | PageRank | References |
16 | 1.08 | 14 |
Authors | ||
5 | ||
Name | Order | Citations | PageRank |
|---|---|---|---|
| Peter Benner | 1 | 825 | 114.06 |
| Pablo Ezzatti | 2 | 124 | 28.24 |
| Daniel Kressner | 3 | 449 | 48.01 |
| Enrique S. Quintana-Orti | 4 | 405 | 32.27 |
| Alfredo Remón | 5 | 95 | 15.95 |