Derivative of interpolating polynomial

[Christopher Kolago]

Let's assume that we have got small number of equally spaces samples of the form (x_0 + i*h, f(x_i)), for some given spacing h and some unknown function f. Is there any theorem that states whether it is better to use

(i) derivative of the interpolating polynomial of these samples,
(ii) interpolating polynomial of differences between values of consecutive samples,

to find a point (possibly between the samples) in which sampled unknown function is increasing most/fastest?

[Torsten Hennig]

Getting the derivatives of a function for which only
(usually noisy) measurements at discrete points
are available is a very difficult task in numerical
analysis.
If your discrete points don't look noisy, you can try
to take the derivative an interpolating
(usually cubic) spline through the sample points.
Otherwise you will have to refer to approximating
splines where - dependent on the strength of the
noise - a reasonable balance is taken between
interpolation and noise reduction.

Best wishes
Torsten.

[Han de Bruijn]

On Jan 25, 9:46 am, Torsten Hennig <Torsten.Hen...@umsicht.fhg.de>
wrote:

Don't think so. Take a look at:

http://hdebruijn.soo.dto.tudelft.nl/www/programs/delphi.htm#ND

Especially note what the software can do for you eventually.

More tedious mathematics about the same at:

http://hdebruijn.soo.dto.tudelft.nl/jaar2010/dikte/document.pdf
http://hdebruijn.soo.dto.tudelft.nl/jaar2010/kammen/document.pdf

Han de Bruijn