Inverse functions of polynomials and its applications to initialize the search of solutions of polynomials and polynomial systems
The authors continue their study of an algorithm for solving polynomial equations based on the Taylor series of the inverse function of a polynomial in the neighborhood of a given point. The main motivation is that the approximate evaluation of this Taylor series at zero can be utilized to find initial approximations for Newton's method. Upper and lower bounds are established for this evaluation. The new proofs of the theorems involved in the construction of the inverse (appeared in previous publications) are given. They provide a better radius of convergence of its Taylor series. More importantly, they present a more general perspective that could allow its application to non-polynomial equations that the authors are working on. Finally, the authors also reexamine the problem of solving polynomial systems using these inverse functions. The new approach can ease the complexity of how they treat it in previous works.
scientific article; zbMATH DE number 5956862