Talk:Aberth method

Untitled
This page could benefit from at least two more items:

1. A little more information on how the initial z_k values are chosen. Currently, the page just states that they are possible to compute, which is not useful for someone wanting to implement the method.

2. The formula for computing w_k involves evaluating p(x_k) and p'(x_k). What are those? Should it say p(z_k) and p'(z_k) instead?

//T —Preceding unsigned comment added by 82.182.96.93 (talk • contribs)


 * 1) One can estimate the size of the roots from the size of the coefficients. Chose the initial points randomly inside the disk of the root radius or perhaps of 1.2 the root radius. The cited paper uses some Gräffe iterations to get a better estimate on the distribution of th roots and chooses initial points accordingly. Using the tangent version of the Graeffe iteration one could even guess approximations for the roots.
 * 2.) Of course, that should be consistent.--LutzL (talk) 12:26, 20 April 2008 (UTC)

Who's Aberth?
The first thing one notices in this article is the absence of the phrase that says
 * , named after ?????? Aberth,
 * , named after ?????? Aberth,

(with a link if the person should have a Wikipedia article. Michael Hardy (talk) 18:27, 19 September 2009 (UTC)

Ehrlich-Aberth vs Aberth-Ehrlich
The method is often referred to as Ehrlich-Aberth method and not just Aberth-Ehrlich method, Google Scholar search for papers related to Ehrlich and Aberth. Are these the same method?

If so, I would add it to the introduction. 2001:638:807:507:4C70:169A:5BB6:8163 (talk) 12:26, 6 September 2022 (UTC)