non-linear fit to find constants in the equation

I am trying to implement the following equation:

U = C1 + C2*E+ C3*E^2 + C4*E^3 + C5*E^4, where U and E is known (10 set of values , 10 x 2).

I need to get the constants C1 to C5. Tried fitnlm with no success. Looking forward to get your help.

Example data set:

U E

2.019 1.615

2.622 1.662

3.358 1.706

4.36 1.759

5.621 1.814

7.324 1.877

9.379 1.94

12.121 2.011

15.364 2.081

20.101 2.167

Answer 1

[Torsten]

E =...;  % column vector
U =...;  % column vector
A = [ones(numel(E),1), E, E.^2, E.^3, E.^4];
b = U;
sol = A\b;
C1 = sol(1)
C2 = sol(2)
C3 = sol(3)
C4 = sol(4)
C5 = sol(5)
p = [C5 C4 C3 C2 C1];
Usim = polyval(p,E);
plot(E,U,E,Usim)

[Baris Gungordu]

Thanks. Similarly, how do we fit the following:

n = (mu*b*C)/(1+b*C)

where we have an array of 13x1 for n and C and trying to find constants of mu and b. Probably a non-linear fitting function will be needed, I am guessing.

Many thanks.

[Torsten]

help lsqcurvefit

[Baris Gungordu]

does it work for non-exponential equations? I could not find an for it without exponentials.

[Torsten]

Cdata = ...;
ndata = ...;
fun = @(p,Cdata)p(1)*p(2)*Cdata./(1+p(2)*Cdata);
p0 = [1, 1];
p = lsqcurvefit(fun,p0,Cdata,ndata)

[Baris Gungordu]

Thanks but it is only returning the initial conditions (p0).

[Torsten]

Maybe the initial guess p0 is far off. Try to use a better p0-vector.