Math. function maker urgently required!

Bernard, What is the maximum allowable normalized error of the function? By normalized error, I mean (Yapprox-Yexact)/Yexact. Regards, Jon

This is generically called "curve fitting". Polynomials are a special (easy) case.

In your example data, I see X changing by 2 orders of magnitude and Y1 changing by 9 orders of magnitude. This strongly implies that the function that you fit with should have some physical justification, e.g. just a polynomial won't stand much chance of being useful and even choosing logs/exponents may not be of much use either (certainly not for extrapolation, possibly of use for interpolation.)

Tim.

There are an infinite number of multiple-input, single-output functions out there. You aren't clear, however, on whether your function is known or if you're trying to find it. If the function is known then you should be able to use just about any software package to generate it.

If you're trying to _find_ the function from data then Matlab can do it as well as anything else; you just may have to write the code yourself. Multivariate function finding would be quite a minefield. I wouldn't try it from data alone -- you should have some idea about the process that generates the data, and if you can't exactly model it with a fixed function you should at least attempt to separate it into smaller chunks that can be found independently.

There's an applied math newsgroup that may be good to ask this question on.

First you say you do not want a polynomial, then you say you do not care "how many coefficient this function may have". Make up your mind.

There are interpolating and approximating functions, BTW.

Rene