Approximating zeros of an analytic function by homotopy method (Q914334)

Like the method of \textit{L. M. Delves} and \textit{J. N. Lyness} [Math. Comp. 21, 543-560 (1967; Zbl 0153.179)] the one proposed here is based on applying the residue theorem to \(z^ kf'(z)/f(z)\), \(k=0,1,...,s\), and an appropriately chosen closed contour C. To find M roots inside C simultaneously one has to set up and solve a polynomial equation of degree M. Using strong classical algebraic results the author derives a special homotopy method that allows him to convert the problem to a system of ordinary differential equations which he then solves numerically with standard software.