CS3414 Afterclass Notes --- 28 May, 2002

1. Introduction (last time)

2. Polynomial interpolation

   1. Facts

      • Good news: polynomials are an attractive choice for interpolation because ...
        • You can fit any n data points with a degree n-1 polynomial.
        • Polynomials are easy to construct and manipulate.

      • Bad news: polynomials are not an attractive choice for interpolation because any problem that involves a high degree polynomial is likely to be very ill-conditioned.

      • Example: famous example (Wilkinson) of just how ill-conditioned a problem it is to work with high-degree polynomials. Perturb a degree 20 polynomial very slightly; some of the roots of that polynomial change dramatically.