On the Bernoulli–Euler–Lagrange–Aitken numerical method for roots of polynomials-Reference-Cited by-同舟云学术

On the Bernoulli–Euler–Lagrange–Aitken numerical method for roots of polynomials

Published:2023-10-30 Issue:5 Volume:67 Page:359-365
ISSN:2524-2431
Container-title:Doklady of the National Academy of Sciences of Belarus
language:
Short-container-title:Dokl. Akad. nauk

Author:

Lebedev A. V.¹,Trubnikov Yu. V.²,Chernyavsky M. M.²

Affiliation:

1. Belarusian State University

2. Vitebsk State University named after P. M. Masherov

Abstract

The article presents a development of the Euler–Lagrange method for calculation of all roots of an arbitrary polynomial P(z) with complex coefficients based on the calculation of the limits of ratios of determinants (as in the Bernoulli–Aitken–Nikiporets methods) built by means of the Taylor and Laurent series coefficients for the function P′(z) / P(z).

Publisher

Publishing House Belorusskaya Nauka

Subject

General Medicine

Reference10 articles.

1. Bernoulli D. Observationes de serbus recurrentibus. Novi Commentarii Academiae Scientiarum Imperialis Petropolitanae, 1732 (1728), no. 3, pp. 85–100.

2. McNamee J. M., Pan V. Y. Numerical methods for roots of polynomials, part II. Boston, Amsterdam, Oxford, 2013. 741 p.

3. Euler L. Introduction to the analysis of infinite (in two volumes). Vol. 1. Moscow, 1961. 315 p. (in Russian).

4. Lagrange J. L. Sur la Méthode d’Approximation tirée des séries récurrentes (1798). Traité de la résolution des équations numériques de tous les degrés. Paris, 1826, vol. 6, pp. 130–137.

5. Aitken A. C. On Bernulli’s Numerical Solution of Algebraic Equations. Proceedings of the Royal Society of Edinburgh, 1927, vol. 46, pp. 289–305. doi: 10.1017/s0370164600022070