Solving a centred and scaled fit

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Rebecca le 11 Avr 2016

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https://fr.mathworks.com/matlabcentral/answers/278453-solving-a-centred-and-scaled-fit

Using the following code, I fit a second order exponential [ f1(x) = a*exp(b*x) + c*exp(d*x) ] to my first set of data and solve the expression to find the value of x for which f1(x) = 100:

fit_f1 = fit(A, B, 'exp2');
a = fit_f1.a;
b = fit_f1.b;
c = fit_f1.c;
d = fit_f1.d;
syms x
eqn = a*exp(b*x) + c*exp(d*x) == 100;
solx = solve(eqn,x)

In the fitting a fifth order polynomial [ f2(x) = p1*x^5 + p2*x^4 + p3*x^3 + p4*x^2 + p5*x + p6 ] to my second set of data, I received the warning that 'the equation was badly conditioned', so centred and scaled my data.

Again, I need to solve the resulting expression to find the value of x for which f2(x)=79. Presumably, prior to doing this, I need to take into account the fact that I scaled and centred the data in the curve fitting... I am however, a little stuck on how to do this...I know that the command [p,S,mu] = polyfit(x,y,n), the centering and scaling values are returned in mu...and a polynomial can be evaluated at the point x using y = polyval(p,x,[],mu)...but I am attempting to go the other way!?!

So, any pointers on how to account for the scaling and centering in a curve fitting when solving the expression of the curve would be really appreciated.