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Wilkinson's PolynomialIn 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.
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