# finding a function from observed values

• Mar 25th 2010, 12:02 PM
geordief
finding a function from observed values
Suppose you have a situation with many variables.
And suppose you have values of this situation for any value of time 9or possible a different variable) that you care to choose..
Is it possible for a computer to match a function from its database as being the nearest match to the results as they are added?
And is it feasible that the function that emerged could be used as a close solution to the problem?
I assume that the computer would have a database of all the known (and extrapolated ) functions that had been imagined in mathematical history.
Am I just looking at an absurdly large computer or is it possible that a simplified versin might cope with small tasks?
• Mar 26th 2010, 02:27 AM
geordief
having just watched the BBC 4 programme ( BBC - BBC Four Programmes - The Secret Life of Chaos ) The Secret Life of Chaos would it be realistic for the computer to approach the best suited function by way of an evolutionary process?
That would avoid the computer having to trial so many functions I would have thought - just persis with and hone those that were initially more successful...
• Mar 26th 2010, 07:39 AM
HallsofIvy
Well, first you would have to define what you mean by "best suited function"- that is, how you would judge between two functions.

Given any finite number of data points, there is always a polynomial that exactly fits those points.
• Mar 26th 2010, 01:51 PM
geordief
well I imagine that the test would be as to which function came closest to solving a new observed .value correctly -so the error would need to be the lowest