Using fsolve for an underdetermined system

I have used fsolve to solve a system of 8 equations for 8 unknowns. I have then extended the system so that I have 16 unknowns but only 14 equations. Fsolve finds a solution so I think it must be optimising something but I can't seem to find out what it is? Does anyone know what Matlab does when it has an underdetermined system?!

Answer 1

[Sean de Wolski]

From the doc:

doc fsolve

The Algorithm option specifies a preference for which algorithm to use. It is only a preference because for the trust-region-reflective algorithm, the nonlinear system of equations cannot be underdetermined; that is, the number of equations (the number of elements of F returned by fun) must be at least as many as the length of x. Similarly, for the trust-region-dogleg algorithm, the number of equations must be the same as the length of x. fsolve uses the Levenberg-Marquardt algorithm when the selected algorithm is unavailable. For more information on choosing the algorithm, see Choosing the Algorithm

[Helena]

Hi Sean, I saw this in the documentation but can't seem to find out what that algorithm actually optimises?

[Sean de Wolski]

It will exit when one the criteria for exitting are met. If you get the exitflag and the output there are probably some hints in there.