Geodesic
On the Hadamard and Vandermonde determinants and the Bernoulli--Euler--Lagrange--Aitken method
Matematičeskie zametki, Tome 116 (2024) no. 1, pp. 91-108

Voir la notice de l'article provenant de la source Math-Net.Ru

The article develops an Euler–Lagrange method for calculating all the roots of an arbitrary polynomial $P(z)$ with complex coefficients. The method is based on calculating the limits of ratios of determinants (as in the Bernoulli–Aitken methods) constructed from the coefficients of the Taylor and Laurent series expansions of the function $P'(z)/P(z)$.
Keywords: root of polynomial, Taylor series, Vandermonde determinant.
Mots-clés : Laurent series, Hadamard determinant 
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     title = {On the {Hadamard} and {Vandermonde} determinants and the {Bernoulli--Euler--Lagrange--Aitken} method},
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     year = {2024},
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A. V. Lebedev; Yu. V. Trubnikov; M. M. Chernyavsky. On the Hadamard and Vandermonde determinants and the Bernoulli--Euler--Lagrange--Aitken method. Matematičeskie zametki, Tome 116 (2024) no. 1, pp. 91-108. http://geodesic.mathdoc.fr/item/MZM_2024_116_1_a6/