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How to fit data to a second degree polynomial equation with 9 co-efficients

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Nik
Nik 2014-6-10
编辑： Roger Wohlwend 2014-6-10
Hello,
I have data for one independent variable and one dependent variable. I need to fit this data to a 9 coefficient second degree polynomial equation.
My equation is of the form Y = [A + Bx + C(x^2)]+[D + Ex + F(x^2)]+[G + Hx + I(x^2)]
x is the independent variable and Y is dependent. I have the values of Y for 10 values of x.
Any suggestions/ help/ recommendations would be greatly appreciated. Is there any way the value of the co-efficients can be found without having to guess the initial values of the co-efficients?
Thanks very much.
Nik.

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Roger Wohlwend
Roger Wohlwend 2014-6-10
There is no unique solution for your equation. So you cannot estimate the coefficients.
What you can do is estimating the following equation: Y = R + Sx + T(x^2). Use linear regression, then it is not necessary to guess initial values.
  2 个评论
Nik
Nik 2014-6-10
Hey Roger,
Thanks for the answer!
Using the 'Y = R + Sx + T(x^2)' will leave me with 3 equations (equations for R, S and T) and 9 unknowns (A to I from my initial question). I need the values of the co-efficients. Can I use something like the 'polyfit' or 'cftool' to get the values that I need?
Thanks again!
Roger Wohlwend
Roger Wohlwend 2014-6-10
编辑：Roger Wohlwend 2014-6-10
No, you can't. All you can do is fit the equation Y = R + Sx + T(x^2). In your original equation with 9 coefficients you have three constants, three linear terms and three quadratic terms:
R = A + D + G;
S = B + E + H;
T = C + F + I;
There is no unique solution to that. No algorithm can help you. Your problem is unsolvable.

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