       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
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

```

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