Approximating roots by quadratic iteration

Authors

  • Alfredo Poirier Pontificia Universidad Catolica del Perú.
  • Jesus Torres Pontificia Universidad Catolica del Perú.

DOI:

https://doi.org/10.22199/issn.0717-6279-5447

Keywords:

roots of polynomials, iteration of quadratic polynomials, complex dynamics

Abstract

We apply a coctel of elementary methods to the problem of finding the roots of an arbitrary polynomial. Specifically, we combine properties of the iteration z → z2 + c with rudimentary Galois theory in order to justify an algorithm to find the roots of a complex polynomial.

Author Biographies

Alfredo Poirier, Pontificia Universidad Catolica del Perú.

Departamento de Ciencias, Sección Matemáticas.

Jesus Torres, Pontificia Universidad Catolica del Perú.

Facultad de Ciencias e Ingeniería.

References

L. Carleson and T. Gamelin, Complex Dynamics. Springer, 2013.

S. Lang, Complex Analysis. Addison-Wesley, 1977.

J. Milnor, Dynamics in One Complex Variable: Introductory Lectures. Vieweg, 2000.

A. Poirier, “Approximating square roots”. ProMathematica, vol. 9, no. 17-18, pp. 95-98, 1995. [On line]. Available: https://bit.ly/3l1rCIE

J. Torres, “Approximating roots of polynomials”, Tesis de Licenciatura. Pontificia Universidad Católica del Perú, 2021.

L. R. Turner, Inverse of the Vandermonde matrix with applications. National Aeronautics and Space Administration, 1966. [On line]. Available: https://go.nasa.gov/3mDqlIn

Published

2023-03-27

How to Cite

[1]
A. Poirier and J. . Torres, “Approximating roots by quadratic iteration”, Proyecciones (Antofagasta, On line), vol. 42, no. 2, pp. 407-431, Mar. 2023.

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