How to calculate the roots of an arbitrary polynomial: Hadamard and Vandermonde determinants and Bernoulli – Euler – Lagrange – Aitken type numerical method for roots of polynomials

We develop Euler – Lagrange method and calculate all the roots of an arbitrary complex polynomial $P(z)$ on the base of calculation (similar to the Bernoulli – Aitken methods) of the limits of ratios of Hadamard determinants built by means of coefficients of expansions into Taylor and Laurent series of the function $\frac{P'(z)}{P(z)}$. (A joint work with Yu.V. Trubnikov and M.M. Chernyavsky.)