Why do I receive different results using the NLINFIT function in the Statistics Toolbox 5.0 (R14) and 4.1 (R13SP1)?

I use the following code that contains a call to the NLINFIT function:

x = [1 2 3 4 5 6 7 8 9 10];

y = [0.473 0.929 1.386 1.851 2.323 2.779 3.242 3.706 4.171 4.621];

beta=[200;0.2];   %Initial estimate of beta

beta = nlinfit(x,y,@modelfun,beta);

My objective function "modelfun" is defined as follows:

function yhat=modelfun(beta,x);

e = beta(1);

f = beta(2);

a = 2/e;

b = (4 + x.^2*pi^2/2) / e^2;

c = x*f;

yhat = (1 + a + b).*c;

Executing this code In MATLAB 6.5.1 (R13SP1), I obtain the following:

 beta(1) = 309.0739

 beta(2) = 0.4585

But in MATLAB 7.0 (R14), my results are as follows:

 beta(1) = -2.2763e+007

 beta(2) = 0.4630

Answer 1

[MathWorks Support Team]

The implementation of the NLINFIT function has changed between the Statistics Toolbox 4.1 (R13SP1) and 5.0 (R14). In R13SP1, NLINFIT uses the Gauss-Newton algorithm. In R14, NLINFIT uses the Levenberg-Marquardt algorithm.

Note: the result returned in R14 is in fact better then the result returned by R13SP1. This can be verified by looking at the residues in both cases. In addition note that this example contains multiple minima and the value of the coefficients returned, depends on the initial estimates of the parameters.