13402

Accelerating Polynomial Homotopy Continuation on a Graphics Processing Unit with Double Double and Quad Double Arithmetic

Jan Verschelde, Xiangcheng Yu
Department of Mathematics, Statistics, and Computer Science, University of Illinois at Chicago, 851 South Morgan (M/C 249), Chicago, IL 60607-7045, USA
arXiv:1501.06625 [cs.MS], (26 Jan 2015)

@article{verschelde2015accelerating,

   title={Accelerating Polynomial Homotopy Continuation on a Graphics Processing Unit with Double Double and Quad Double Arithmetic},

   author={Verschelde, Jan and Yu, Xiangcheng},

   year={2015},

   month={jan},

   archivePrefix={"arXiv"},

   primaryClass={cs.MS}

}

Download Download (PDF)   View View   Source Source   Source codes Source codes

Package:

863

views

Numerical continuation methods apply predictor-corrector algorithms to track a solution path defined by a family of systems, the so-called homotopy. The systems we consider are defined by polynomials in several variables with complex coefficients. For larger dimensions and degrees, the numerical conditioning worsens and hardware double precision becomes often insufficient to reach the end of the solution path. With double double and quad double arithmetic, we can solve larger problems that we could not solve with hardware double arithmetic, but at a higher computational cost. This cost overhead can be compensated by acceleration on a Graphics Processing Unit (GPU). We describe our implementation and report on computational results on two benchmark polynomial systems. In case the linear algebra dominates the total computational cost of a path tracker, the dimension needs to be of the order of at least several hundreds to offset the computational overhead caused by double double arithmetic. For general polynomials of higher degrees, when evaluating and differentiating the polynomials is computationally expensive, already in smaller dimensions, acceleration may offset the cost of higher precision arithmetic.
Rating: 2.5/5. From 1 vote.
Please wait...

* * *

* * *

Featured events

2018
November
27-30
Hida Takayama, Japan

The Third International Workshop on GPU Computing and AI (GCA), 2018

2018
September
19-21
Nagoya University, Japan

The 5th International Conference on Power and Energy Systems Engineering (CPESE), 2018

2018
September
22-24
MediaCityUK, Salford Quays, Greater Manchester, England

The 10th International Conference on Information Management and Engineering (ICIME), 2018

2018
August
21-23
No. 1037, Luoyu Road, Hongshan District, Wuhan, China

The 4th International Conference on Control Science and Systems Engineering (ICCSSE), 2018

2018
October
29-31
Nanyang Executive Centre in Nanyang Technological University, Singapore

The 2018 International Conference on Cloud Computing and Internet of Things (CCIOT’18), 2018

HGPU group © 2010-2018 hgpu.org

All rights belong to the respective authors

Contact us: