CS3414 Afterclass Notes --- 28 May, 2002
Fitting Data (parts of Chapters 4, 7, 10)
- Introduction (last time)
- Polynomial interpolation
- Good news: polynomials are an attractive choice for
interpolation because ...
- You can fit any n data points with a degree n-1
- 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