Interpolation

*To*: mathgroup at smc.vnet.net*Subject*: [mg32285] Interpolation*From*: Yas <y.tesiram at pgrad.unimelb.edu.au>*Date*: Fri, 11 Jan 2002 04:35:19 -0500 (EST)*Sender*: owner-wri-mathgroup at wolfram.com

G'day mathgroup, I have some general questions on Interpolation as implemented in Mathematica. Essentially, I have a series of profiles for which I have no general function. The profile is generated by repetitive multiplication of rotation matrices and so it is difficult (and also impractical) to deduce an analytic function. Instead to answer the questions I have, I have decided to use Interpolation -- a pitiful state, nevertheless a shade better than extrapolation. The first step involves creating the Interpolating function, thing1 = Interpolation[data]; Then I find the first derivative, thing2 = D[thing1[x], {x, 0, lastdatapoint}] Next I want to find the points where thing2 = 0, but I have run into problems with Mathematica complaining about inverse functions etc, although plots of thing2 versus x look fine. My primary question is, 1. The profiles that I have, have maxima and minima whose co-ordinates I want to find, hence the differentiation step. Interpolation does a good job reproducing the data points and in finding a derivative that can be plotted but not when asked to Solve for thing2 = 0. How do I go about finding the accuracy of the Interpolating Function to test whether the value near thing2 = 0 is well behaved? And a secondary question is, 2. Is there another efficient method of estimating the co-ordinates of the minima and maxima by computer of data sets? The length of each of these data sets is 1000 points and for that reason I have not pasted it into the email. As a demonstrative example, the Table of values generated by, Table[Sin[0.75 + Exp[Pi*t]], {t, 0, 1, 1/1000}]; ListPlot[%] is closely related. Any help or comments will be appreciated. Thanks Yas