Getting the function back from a table
This probably sounds weird, but are there any Wikipedia articles on the topic of "reconstructing" the function used in a table of values? For example, if I had a table:
x 8 10 12
y 71 97 123
Just in case you didn't know, it means that f(8)=71, f(10)=97, and f(12)=123. I'm trying to find out what the function (f) is. I can then use a certain method to find that the function is . Is there any more information out there on this topic (the "reconstruction")?
--wj32 t/c 02:12, 18 January 2008 (UTC)
It is, in general, impossible, because there are an infinite number of possible functions that satisfy those criteria. However, if you have further ...view middle of the document...
So, now I've got three questions:
Has this stuff been researched before?
Is there a general rule for these formulas that can extend to polynomials of the third or higher degrees?
Do you even understand what I'm saying (mmm)?
--wj32 t/c 03:05, 18 January 2008 (UTC)
Yay I found it (although it's a bit complicated...)! Polynomial interpolation --wj32 t/c 03:11, 18 January 2008 (UTC)
You might find System of linear equations more helpful. With the three equations you get from three data points, you can solve to find the three coefficients of your polynomial, as you have done. Interpolation is sort of related, but I think you more want to know how to find the polynomial itself. Yes, this sort of thing is very well researched and applies to polynomials of any degree, and all sorts of other problems. As the number of equations get large, we have more "automated" ways of solving a system of equations, such as Gaussian elimination. - Rainwarrior (talk) 05:33, 18 January 2008 (UTC)
Thanks, I was just frustrated I couldn't find any info on...