problem using fsolve in parameter identification, is it good to add redundancy?

I want to identify 4 parameters of a nonlinear equations f(x,y)=0. Now I got several groups of experimental data: x and y.

Theoretically, only four groups of x and y is needed to create 4 equations to solve and get the 4 parameters.

But is it better for me to use all the groups of x and y as redundancy in fsolve so that I can get a better identification result? How does fsolve works?

Answer 1

[Shashank Prasanna]

fsolve in some sense tries to force the sum of squares of the output of system to zero. If you have a system of non-linear equations then use FSOLVE. Redundant equations will feature in the optimization during the minimization as well.

On the other hand if you have a single nonlinear equation with 4 parameters and several observations (groups of x and y) and would like to estimate the 4 parameters then use lsqnonlin or nlinfit. Can you give us an idea or an example of your f(x,y)

[Fan]

Thank you very much! And sure,it is expressed by an implicit function like: c1-y-(x+c4*y)/c3-c4*(e^((x+c4*y)/0.026)-1)=0 %c1 c2 c3 c4 are the parameters that will be identified %x is independent variable and y is dependent variable, which are derived by experiment

At first, I tried to use nlinfit, by making both x and y as input and 0 as output, but the result is poor. And that's why I tried to use fsolve.

Do you have any suggestion about this?

[Shashank Prasanna]

Create a system using all your observations. The following function will accept c-the parameters to be optimized, x and y your observation vectors:

function Y = Fcn(c,x,y)

n=length(y);
C = repmat(c(:)',n,1);
Y = C(:,1)-y-(x+C(:,4).*y)./C(:,3)-C(:,4).*(exp((x+C(:,4).*y)/0.026)-1);

end

You will use this function in fsolve as follows:

>> x = rand(100,1);y = rand(100,1); %sample x and y, you'll use your data.
>> c0 = [1 1 1 1] %initial values
>> F = fsolve(@(c)(Fcn(c,x,y)),c0)

[Fan]

Got it! But there's another thing that I am confused about: why the input of fsolve should be an anonymous function? Why it is not able to use the function Fcn directly？

[Shashank Prasanna]

Because you have to pass extra arguments in addition (x,y) to C. This link explains what i am talking about:

http://www.mathworks.com/help/optim/ug/passing-extra-parameters.html

[Fan]

Thank you very much!