#### CS3414 Afterclass Notes --- 28 May, 2002

**Fitting Data** (parts of Chapters 4, 7, 10)
- Introduction (last time)

- Polynomial interpolation

- 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.