Wilkinson's polynomial

In <a href="/facts/Numerical_analysis/QT9cYa9z">numerical analysis</a>, Wilkinson's polynomial is a specific <a href="/facts/Polynomial/Lzak8VVx">polynomial</a> which was used by <a href="/facts/James_H._Wilkinson/4aKUNcrg">James H. Wilkinson</a> in 1963 to illustrate a difficulty when <a href="/facts/Root-finding_algorithm/IxTDkhBq">finding the roots</a> of a polynomial: the location of the <a href="/facts/Root_of_a_polynomial/mlK3dhoT">roots</a> can be very sensitive to perturbations in the <a href="/facts/Coefficient/5Hwq2Wuq">coefficients</a> of the polynomial.
The polynomial is

w
        (
        x
        )
        =
        
          ∏
          
            i
            =
            1
          
          
            20
          
        
        (
        x
        −
        i
        )
        =
        (
        x
        −
        1
        )
        (
        x
        −
        2
        )
        ⋯
        (
        x
        −
        20
        )
        .
      
    
    {\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.

Wilkinson's polynomial open-in-new

Wilkinson's polynomial