Mapping based algorithm for large-scale computation of quasi-polynomial zeros

A method for computing all zeros of a retarded quasi-polynomial that are located in a large region of the complex plane is presented. The method is based on mapping the quasi-polynomial and on utilizing asymptotic properties of the chains of zeros. First, the asymptotic exponentials of the chains are determined based on the distribution diagram of the quasi-polynomial. Secondly, large regions free of zeros are defined. Finally, the zeros are located as the intersection points of the zero-level curves of the real and imaginary parts of the quasi-polynomial, which are evaluated over the areas of the region outside those free of zeros. Index Terms--Function zeros, quasi-polynomial, retarded system, root-finding techniques, spectrum distribution.