An analytic approach to the solution of non-linear equations

摘要

Isolating the zeros of a scalar function analytic on a disk by means of exploring function structure was shown to be very efficient (Klip, 1985). This will be exemplified in this paper on the hand of data obtained with certain test polynomials. It was shown by Klip (1987) that the structure of the zero curves for the polynomial leads to a new formulation of the location of the critical points. It will be proven that the number of critical points in a branch region of order m equals m − 1. Completeness of the tracing is an important issue. We give an account of the design of the completeness algorithm and discuss the role of a small listprocessing system in registering temporarily stored data as well as modifications of the pathways.