Related papers: Numerical approximation of multiple isolated roots…

We explore an algorithm for approximating roots of integers, discuss its motivation and derivation, and analyze its convergence rates with varying parameters and inputs. We also perform comparisons with established methods for approximating…

This paper deals with the use of numerical methods based on random root sampling techniques to solve some theoretical problems arising in the analysis of polynomials. These methods are proved to be practical and give solutions where…

Highly efficient and even nearly optimal algorithms have been developed for the classical problem of univariate polynomial root-finding (see, e.g., \cite{P95}, \cite{P02}, \cite{MNP13}, and the bibliography therein), but this is still an…

The approximation of a multiple isolated root is a difficult problem. In fact the root can even be a repulsive root for a fixed point method like the Newton method. However there exists a huge literature on this topic but the answers given…

In this paper, we propose a new and simple approach to the approximation algorithms that are modified and improved from our published results. The computational and graphical examples are presented with the aid of Maple procedures.

Many statistics of roots of random polynomials have been studied in the literature, but not much is known on the concentration aspect. In this note we present a systematic study of this question, aiming towards nearly optimal bounds to some…

We seek random versions of some classical theorems on complex approximation by polynomials and rational functions, as well as investigate properties of random compact sets in connection to complex approximation.

The analysis of solutions to algebraic equations is further simplified. A couple of functions and their analytic continuation or root findings are required.

We devise a simple but remarkably accurate iterative routine for calculating the roots of a polynomial of any degree. We demonstrate that our results have significant improvement in accuracy over those obtained by methods used in popular…

This brief note corrects some errors in the paper quoted in the title, highlights a combinatorial result which may have been overlooked, and points to further improvements in recent literature.

We combine the known methods for univariate polynomial root-finding and for computations in the Frobenius matrix algebra with our novel techniques to advance numerical solution of a univariate polynomial equation, and in particular…

Given an approximation to a multiple isolated solution of a polynomial system of equations, we have provided a symbolic-numeric deflation algorithm to restore the quadratic convergence of Newton's method. Using first-order derivatives of…

The purpose of this article is to present, in a simple way, an analytic approach to special numbers and polynomials. The approach is based on the derivative polynomials. The paper is, to some extent, a review article, although it contains…

We give a simplified approach to the Abhyankar--Moh theory of approximate roots. Our considerations are based on properties of the intersection multiplicity of local curves.

Univariate polynomial root-finding is both classical and important for modern computing. Frequently one seeks just the real roots of a polynomial with real coefficients. They can be approximated at a low computational cost if the polynomial…

We present an algorithm for computing asymptotic approximations of roots of polynomials with exp-log function coefficients. The real and imaginary parts of the approximations are given as explicit exp-log expressions. We provide a method…

In this article we use a method of finding the index of a complex-valued function by determined number of arithmetic operations to describe an algorithm of localization of roots of square-free polynomials. We give an estimation of the…

We present a new algorithm for reconstructing an exact algebraic number from its approximate value using an improved parameterized integer relation construction method. Our result is consistent with the existence of error controlling on…

We present a complete algorithm for finding an exact minimal polynomial from its approximate value by using an improved parameterized integer relation construction method. Our result is superior to the existence of error controlling on…

Univariate polynomial root-finding is a classical subject, still important for modern computing. Frequently one seeks just the real roots of a real coefficient polynomial. They can be approximated at a low computational cost if the…