If I have a set of n numbers, (n=0,1,2, ... n-1), what is the maximum number coefficients in a series I would need in order to find y=f(n) true on the integers up to n-1? Or is that something I just have to check after fitting it? ( does it need an nth degree polynomial?)(adsbygoogle = window.adsbygoogle || []).push({});

Another question:

If I have a finite set of functions, F_{t}(x), and these functions may or may not be similar (i.e. F_{t}(x) = x, x^{2}, x^{3}... x^{t}), how can I fit a plane to a set of functions such that F(1,x)=F_{1}(x), F(2,x)=F_{2}(x) ... in order to find an equation F(t,x)?

can/how is this done if each function is a summation? (i.e. F_{1}=[itex]\sum[/itex]a_{1}(n)*x^{n}, F_{2}=[itex]\sum[/itex]a_{2}(n)*x^{n})

can I find an equation like F(t,x) = [itex]\sum[/itex]G(t)*a_{t}(n)*x^{n}that will satisfy this?

thanks

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# Curve fitting and Plane fitting

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