A Branch-and-Bound Algorithm for Computing the Reliable Isolated Zeros of Multivariate Polynomial Functions Systems

In this paper, we present an algorithm using the GPGPU machine to compute the interval solutions of isolated real zeros of multivariate polynomial functions in given ranges. To overcome the state space explosion in the process of searching zero points, we combine the branch-and-bound method and the Hansen-Sengupta method, and the interval arithmetic has been used throughout the computation to guarantee the reliability of results. The computation is implemented on GPGPU system, and experiments for 55 benchmark problems have been done. The result shows our method can produce reliable isolation for real zeros in accepted time.