In working with a geologist who had some (discrete) data to understand, and in thinking about presenting the definition of derivative so that students will *understand* it, I ran into this question:
If I have tabular data (x1,y1), (x2,y2) .... (yn = f(xn)) with the xn's NOT equally spaced, what is the "optimal" way to estimate the derivatives at various places? One way is to do quadratic interpolation on each triple of points to estimate the derivative at the middle point. Not being well-versed in numerical techniques, is this a standard approach.
Please do not tell me that there exists a C-infinity function passing through my points with arbitary derivatives. I know that. I'm interested in a situation where the "bumps" are well-recognized in the data (and in formulating this condition as a bound on f'' or something.)
In lieu of discussion, I would appreciate good references, or will any text on "interpolation" fo?
Thanks, and happy holidays.
--- Don Goldberg, Mathematics Dept, Occidental College, Los Angeles CA 90041 email@example.com