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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)

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 NVIDIA Tesla C2050, K20C, and K40 general purpose graphics processing units. As the dimension equals several thousands, the cost to compute one QR decomposition is sufficiently large so that the… (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)

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)

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