A bibliography on roots of polynomials
Journal of Computational and Applied Mathematics
Practical quasi-Newton methods for solving nonlinear systems
Journal of Computational and Applied Mathematics - Special issue on numerical analysis 2000 Vol. IV: optimization and nonlinear equations
A Family of Scaled Factorized Broyden-Like Methods for Nonlinear Least Squares Problems
SIAM Journal on Optimization
On Sizing and Shifting the BFGS Update within the Sized-Broyden Family of Secant Updates
SIAM Journal on Optimization
Tensor-Krylov Methods for Solving Large-Scale Systems of Nonlinear Equations
SIAM Journal on Numerical Analysis
On Convergence of the Additive Schwarz Preconditioned Inexact Newton Method
SIAM Journal on Numerical Analysis
Modified Newton's method for systems of nonlinear equations with singular Jacobian
Journal of Computational and Applied Mathematics
An algorithm to initialize the searchof solutions of polynomial systems
Computers & Mathematics with Applications
Computers & Mathematics with Applications
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In this paper we present a new algorithm for solving polynomial equations based on the Taylor series of the inverse function of a polynomial, f P (y). The foundations of the computing of such series have been previously developed by the authors in some recent papers, proceeding as follows: given a polynomial function $y=P(x)=a_0+a_1x+\cdots+a_mx^m$ , with $a_i \in \mathcal{R}, 0 \leq i \leq m$ , and a real number u so that P驴(u)驴驴驴0, we have got an analytic function f P (y) that satisfies x驴=驴f P (P(x)) around x驴=驴u. Besides, we also introduce a new proof (completely different) of the theorems involves in the construction of f P (y), which provide a better radius of convergence of its Taylor series, and a more general perspective that could allow its application to other kinds of equations, not only polynomials. Finally, we illustrate with some examples how f P (y) could be used for solving polynomial systems. This question has been already treated by the authors in preceding works in a very complex and hard way, that we want to overcome by using the introduced algorithm in this paper.