Publication IEICE TRANSACTIONS on Fundamentals of Electronics, Communications and Computer SciencesVol.E80-App.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 DCn. 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.