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

Authors:
Feifei Wei;Jieqing Feng;Hongwei Lin
Affiliations:
-;-;-
Venue:
Computers & Mathematics with Applications
Year:
2011

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Abstract

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.