A Path Following Algorithm for Finding All the Solutions on Non-linear Equation System in a Compact Region

Hisato FUJISAKA  Hisakazu NISHINO  Chikara SATO  Yuuji SATOH  

Publication
IEICE TRANSACTIONS on Fundamentals of Electronics, Communications and Computer Sciences   Vol.E80-A       pp.2308-2317
Publication Date: 1997/11/25
Online ISSN: 
DOI: 
Print ISSN: 0916-8508
Type of Manuscript: Category: Numerical Analysis and Optimization
Keyword: 
continuous deformation,  degree of function,  

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Summary: 
We propose a method to search all the zeros of a complex function in a given compact region D Cn. The function f: Cn Cn to be considered is assumed to consist of polynomial and transcendental terms and to satisfy f (x) Rn for any x Rn. Using the properties of such a complex function, we can compute the number of zeros and determine the starting points of paths on the boundary of D, which attain all the zeros of f in D without encountering a singular point. A piecewiselinear approximation of the function on a triangulation is used for both computing the number of zeros and following the paths.