Home > Wilkinson's polynomial

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.