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The usual methods for root finding of polynomials are based on the iterationof a numerical formula for improvement of successive estimations. Theunpredictable nature of the iterations prevents to search roots inside apre-specified region of complex plane. This work describes a root findingmethod that overcomes this disadvantage. It is based on the winding number ofplane curves, a geometric construct that is related to the number of zeros ofeach polynomial. The method can be restrained to search inside a pre-specifiedregion. It can be easily parallelized. Its correctness is formally proven, andits computational complexity is also analyzed.

A Geometrical Root Finding Method for Polynomials, with Complexity Analysis