Talk:Aberth method

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 Field: Analysis

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 (talkcontribs)

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?[edit]

The first thing one notices in this article is the absence of the phrase that says

, named after ?????? Aberth,

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