GRPF: Global Complex Roots and Poles Finding Algorithm Based on Phase Analysis.

A flexible and effective algorithm GRPF (Global complex Roots and Poles Finding) for complex roots and poles finding is presented. A wide class of analytic functions can be analyzed, and any arbitrarily shaped search region can be considered. The method is very simple and intuitive. It is based on sampling a function at the nodes of a regular mesh, and on the analysis of the function phase. As a result, a set of candidate regions is created and then the roots/poles are verified using a discretized Cauchy's argument principle. The accuracy of the results can be improved by the application of a self-adaptive mesh. The effectiveness of the presented technique is supported by numerical tests involving different types of functions (microwave and optical applications). The results are verified, and the computational efficiency of the method is examined.