People, 1st time on researchgate so aloha to all!!
The Question:
I have a certain data set and I am using Thiele's rational Polynomial Interpolation to interpolate some data but the curve will fit best depending on good point selection. So is there any particular algorithm to select best fitting interpolation points beforehand?
Yeah That's It!!
:-)
PS:- I plan to use Mean Value Theorem to get the best points (where 1st derivative is zero relative to starting and ending points of the interpolation) but are there any other methods?
Dear Peter:-
Sorry for the delay to reply.. Took some time to digest the whole info in your reply since I do not come from much of a mathematical background.. Thanks a whole lot!
By the way we saw about this "Thiele Werner" method of interpolation in some research papers and yes I was indeed talking about this newton/thiele continuous fraction method mentioned in wikipedia.
A first question is why you are using Rational Polynomial interpolation, i.e. what conditions are you wanting to impose on the interpolating curve? You might want to look at the Radial Basis function literature, this includes splines as a special case. I am guessing that your problem is in 2 D, i.e. that the data will consist of pairs (x,y).
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