Implementation of the "Sums of Powers Algorithm" for the efficient and reliable approximation of all polynomial roots as an alternative to the kernel function "laguerre"

[Herbert Möller <herbert.moeller@…>]

The Sums of Powers Algorithm (SPA) is the only efficient and reliable algorithm for the approximation of all polynomial roots. It was first published in my book ''Algorithmische Lineare Algebra'', Verlag Vieweg, Wiesbaden 1997. The article ''

[Herbert Möller <herbert.moeller@…>]

Actual version of the Sums of Powers Algorithm

[Herbert Möller <herbert.moeller@…>]

The Sums of Powers Algorithm (SPA) is the only efficient and reliable algorithm for the approximation of all polynomial roots. It was first published in my book "Algorithmische Lineare Algebra", Verlag Vieweg, Wiesbaden 1997. The article "An Efficient and Reliable Algorithm for the Approximation of all Polynomial Roots Based on the Method of D. Bernoulli" in the journals Sovremennye Problemy Matematiki, 2012, Vol. 16, pp. 52-65, and Proceedings of the Steklov Institute of Mathematics, 2013, Vol. 280, Suppl. 2, pp. S43-S55, contains an actual version of the SPA. Moreover a Maple program and its documentation "Visualization of the First Stage of the SPA" are available in the website "Mathkompass". Since the beginning of an URL is blacklisted, the URLs can't be given here.