The simplest approach is to do some kind of spline interpolation like Jim Clay suggests (linear or otherwise). However, if you have the luxury of batch processing, and especially if you have an overdetermined set of nonuniform samples, there's a "perfect reconstruction" algorithm that's extremely...
This question is intimately connected with previous one: "How to create internally optimized expression for computing with high WorkingPrecision?"
Oleksandr R. correctly states in the comment:
A good answer will hopefully discuss the
Experimental`NumericalFunction, which is a structure pro...
@OleksandrR. I wish that were true. I found it very difficult to work out what the difference between Mathematica and the Finance Platform was, other than the Bloomberg Link. Even the Wolfram staff I spoke to about it struggle to articulate it.
As I said earlier, I'm intrigued by the Data Science platform too - we are likely to have some VERY big data to deal with soon. But what worries me is that Wolfram is getting all Microsofty on us, with "products" for finance, data science, this that and the other, when all it is is the one core product plus one add-on. So you don't know which to choose in case you need something from the another of the products.
Don't they realise that the integration and not having to buy all sorts of different add-ons to get full functionality is one of the advantages Mathematica has over Matlab.