Inverse functions of polynomials and its applications to initialize the search of solutions of polynomials and polynomial systems
type: Item
instance of: scholarly article
title: Inverse functions of polynomials and its applications to initialize the search of solutions of polynomials and polynomial systems
zbMATH Open document ID: 1231.65082
author: Juan-Miguel Gracia
published in: Numerical Algorithms
publication date: 2011-10-11T00:00:00Z
full work available at URL: http://hdl.handle.net/10251/49340
review text: 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.
Mathematics Subject Classification ID: 65H04
Mathematics Subject Classification ID: 65H10
Mathematics Subject Classification ID: 26C10
zbMATH DE Number: 5956862
zbMATH Keywords: Newton's method
zbMATH Keywords: quasi-Newton methods
zbMATH Keywords: inverse function of polynomials
zbMATH Keywords: polynomial zeros
zbMATH Keywords: polynomial systems zeros
zbMATH Keywords: algorithms
zbMATH Keywords: nonlinear equations
MaRDI profile type: Publication
OpenAlex ID: W1984419959
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DOI: 10.1007/S11075-011-9453-X
description: scientific article; zbMATH DE number 5956862