Efficient polynomial root finding using SIMD extensions

In this paper, the parallel implementations of different iterative polynomial root finding methods on a processor with SIMD processing capability are reported. These methods are based on the construction of a sequence of approximations that converge to the set of roots. We have chosen four widely used methods namely Newton´s, Durand-Kerner´s, Aberth-Ehrlich´s, and QD and implemented them using the SIMD instruction set of the Pentium processor with C++ and assembly language. Experiments show that a speedup of 3 or higher can be achieved, depending on the order of polynomial, required accuracy, and the method employed.