I need to do a polynomial interpolation of a set of $N$ 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 over-determined. Does anyone have an idea of what should be done in such case (supposing it is even possible)?