Semenov, Vasyl Method for the calculation of all zeros of an analytic function based on the Kantorovich theorem. (English) Zbl 1297.65055 Comput. Methods Appl. Math. 14, No. 3, 385-392 (2014). Summary: We propose a method to calculate all zeros of an analytic function in a given rectangle. The main idea of our method is to construct a covering of the initial rectangle by subsets where either there are no zeros or the zero uniqueness test based on the Kantorovich theorem is satisfied. The algorithm for the construction of such covering is presented. The implementation of the method is shown on different examples. Cited in 2 Documents MSC: 65H05 Numerical computation of solutions to single equations 65E05 General theory of numerical methods in complex analysis (potential theory, etc.) 30C15 Zeros of polynomials, rational functions, and other analytic functions of one complex variable (e.g., zeros of functions with bounded Dirichlet integral) Keywords:nonlinear equation; localization of roots; Kantorovich theorem; Taylor’s expansion; complex roots; numerical examples; analytic function; algorithm PDFBibTeX XMLCite \textit{V. Semenov}, Comput. Methods Appl. Math. 14, No. 3, 385--392 (2014; Zbl 1297.65055) Full Text: DOI