CS3414 Afterclass Notes --- 24 May, 2002
Fitting Data (parts of Chapters 4, 7, 10)
given a discrete set of data points
(xi,yi), for i = 1, 2, ..., m;
find a function g(x) that either:
- matches exactly (interpolates) the given data, or
- approximates the given date in some sense (e.g., in
the least squares sense).
- Method of undetermined coefficients: a generic approach to
finding g(x) that satisfies certain properties (like interpolation).
- Choose a set of basis functions to be used to represent g(x).
We will write g(x) as a linear combination of these basis
g(x) = a1 b1(x) +
a2 b2(x) + ... +
- Enforce n constraints or conditions that you want g(x) to
satisfy. The goal is to derive n linear equations in the
n unknowns a1, ..., an. For example,
in the case of interpolation, we would want n=m and
g(xi) = yi, for i = 1, ..., n.
- What's left to talk about ?
- What are good choices for the basis functions (with respect
to cost/efficiency and accuracy)?
- Which is more important---cost to construct g(x) or cost to
- Is it easy to add new data points to my model?
- What if I only want to approximately match the data?