I need to do a polynomial interpolation of a set $N$ of experimental points; the functional form I have to use to interpolate is this: $$ f(x) = a + bx^2 + cx^4,$$ as you can see the coefficient that I need to find are just 3: $a, b, c$; however the points I have are $\#N>3$ and so it looks like the determination of the coefficients is impossible because is over-determined. Does anyone have an idea of what should be done in such case (supposing it is even possible)?
Since the system is overdetermined, there is ideally no solution.Hoever things like least square fit etc. are still possible, and this will be fitting a polynomial to a given graph. An easy way would be to treat it like a linear equation (trat 1, x, x^2 as columns of matrix) and then solve using Y=bX. X wont be invertible, but use any matrix algebra package to find least square solution.