Wilkinson's polynomial

Graph of Wilkinson's polynomial

Graph of ${\displaystyle \operatorname {sgn}(w(x))\ln(1+|w(x)|)}$

In numerical analysis, Wilkinson's polynomial is a specific polynomial which was used by James H. Wilkinson in 1963 to illustrate a difficulty when finding the roots of a polynomial: the location of the roots can be very sensitive to perturbations in the coefficients of the polynomial.

The polynomial is $${\displaystyle w(x)=\prod _{i=1}^{20}(x-i)=(x-1)(x-2)\cdots (x-20).}$$ Sometimes, the term Wilkinson's polynomial is also used to refer to some other polynomials appearing in Wilkinson's discussion.