AN ALGORITHM FOR FINDING ALL ZEROS OF ANALYTIC FUNCTIONS AND ITS COMPLEXITY ANALYSIS
一个寻求解析函数零点的单纯同伦算法及复杂性分析

This paper presents a global algorithm for numerically Obtaining all zeros ofan analytic function in a compact region over the complex plane by use of the complex degreereported in paper 6]. A great deal of numerical examples as well as the conve?enceanalysis imply that this simple algorithm is safe and efficient, and is of moderate computa-tional cost. Furthermore, when this algorithm is,used to determine all zeros of an algebraicpolynomial, a triangular polynomial; or an exponential polynomial, the safe grid size of thetriangulation involved in the algorithm can be easily estimated. Our results also show thealgorithm proceeds well with the 2-dimensional compact manifold having boundaries.