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)?
2026-03-27 16:19:13.1774628353
Trouble doing polynomial interpolation
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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.