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GPU-based parallel solver via the Kantorovich theorem for the nonlinear Bernstein polynomial systems

Feifei Wei, Jieqing Feng, Hongwei Lin
State Key Lab of CAD&CG, Zhejiang University, 310058, China
Computers & Mathematics with Applications, Volume 62, Issue 6, Pages 2506-2517, 2011

@article{wei2011gpu,

   title={GPU-based parallel solver via the Kantorovich theorem for the nonlinear Bernstein polynomial systems},

   author={Wei, F. and Feng, J. and Lin, H.},

   journal={Computers & Mathematics with Applications},

   year={2011},

   publisher={Elsevier}

}

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This paper proposes a parallel solver for the nonlinear systems in Bernstein form based on subdivision and the Newton-Raphson method, where the Kantorovich theorem is employed to identify the existence of a unique root and guarantee the convergence of the Newton-Raphson iterations. Since the Kantorovich theorem accommodates a singular Jacobian at the root, the proposed algorithm performs well in a multiple root case. Moreover, the solver is designed and implemented in parallel on Graphics Processing Unit(GPU) with SIMD architecture; thus, efficiency for solving a large number of systems is improved greatly, an observation validated by our experimental results.
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