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MathGroup Archive 2002

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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



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