A PATH-FOLLOWING ALGORITHM FOR FINDING ALL THE SOLUTIONS OF NONLINEAREQUATION SYSTEM IN A COMPACT REGION

We propose a method to search all the zeros of a complex function in a given compact region D subset of C-n. The function f : C-n --> C-n to be considered is assumed to consist of polynomial and transcendental terms and to satisfy f(x) is an element of R-n for any x is an element of R-n. Using the properties of such a complex function, we can compu te the number of zeros and determine the starting points of paths on t he boundary of D, which attain all the zeros of f in D without encount ering a singular point. A piecewise-linear approximation of the functi on on a triangulation is used for both computing the number of zeros a nd following the paths.