A reliable algorithm for computing the topological degree of a mapping in R2

K.H. Ko, T. Sakkalis, N.M. Patrikalakis
2008 Applied Mathematics and Computation  
In this paper, we present a method to reliably compute the topological degree of a mapping in the plane, over a simple closed polygon. The method is based on Henrici's argument principle, and computes the degree using the winding number concept in range arithmetic. The algorithm is then applied to the root computation of a univariate polynomial. The proposed algorithms are demonstrated with examples.
doi:10.1016/j.amc.2007.07.002 fatcat:t7mnljqarffonawvdfhglycniu