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Wilkinson's polynomial
In numerical analysis, Wilkinson's polynomial of degree k is given by the formula
which has k roots: 1, 2, ..., k.
The problem of finding the roots is ill-conditioned. A small change in one coefficient can lead to drastic changes in the roots found by root-finding algorithms.
Wilkinson's polynomial of degree 20 has 20 roots, but, as the graph below shows, the function becomes almost horizontal near the x-axis.
In 1984, James H. Wilkinson admitted
- Speaking for myself I regard it as the most traumatic experience in my career as a numerical analyst.
Last updated: 06-01-2005 20:55:25
11-30-2008 18:11:33
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The contents of this article is licensed from www.wikipedia.org under the GNU Free Documentation License. Click here to see the transparent copy and copyright details