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- Jan Verschelde, Xiangcheng Yu
- PASCO
- 2015

Numerical continuation methods track a solution path defined by a 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… (More)

- Jan Verschelde, Xiangcheng Yu
- 2014 IEEE Intl Conf on High Performance Computing…
- 2014

In order to compensate for the higher cost of double double and quad double arithmetic when solving large polynomial systems, we investigate the application of the NVIDIA Tesla K20C graphics processing unit (GPU). The focus on this paper is on Newton's method, which requires the evaluation of the polynomials, their derivatives, and the solution of a linear… (More)

Polynomial systems occur in many areas of science and engineering. Unlike general nonlinear systems, the algebraic structure enables to compute all solutions of a polynomial system. We describe our massive parallel predictor-corrector algorithms to track many solution paths of a polynomial homotopy. The data parallelism that provides the speedups stems from… (More)

- Nathan Bliss, Jeff Sommars, Jan Verschelde, Xiangcheng Yu
- CASC
- 2015

Polynomial systems occur in many fields of science and engineering. Polynomial homotopy continuation methods apply symbolic-numeric algorithms to solve polynomial systems. We describe the design and implementation of our web interface and reflect on the application of polynomial homotopy continuation methods to solve polynomial systems in the cloud. Via the… (More)

- Jan Verschelde, Xiangcheng Yu
- 2015 IEEE 17th International Conference on High…
- 2015

Polynomial systems occur in many areas of science and engineering. Unlike general nonlinear systems, the algebraic structure enables to compute all solutions of a polynomial system. We describe our massively parallel predictor-corrector algorithms to track many solution paths of a polynomial homotopy. The data parallelism that provides the speedups stems… (More)

- Jan Verschelde, Xiangcheng Yu
- ACM Comm. Computer Algebra
- 2015

The purpose of the software presentation is to announce a library to track many solution paths defined by a polynomial homotopy on a Graphics Processing Unit (GPU). Developed on NVIDIA graphics cards with CUDA SDKs, our code is released under the GNU GPL license. Via the C interface to PHCpack, we can call our GPU library from Python.

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