title: Matlab's fsolve converges *but* seems to give wrong solution
body: <p>I am trying to solve a system of non linear equations using fsolve; lets say</p>
  
  <p>F(x;lambda) = 0, where lambda is a vector of parameters, and x the vector I want to solve for.</p>
  
  <p>I am using Matlab's fsolve.</p>
  
  <p>I have 2 values of the parameter lambda, that I want to solve the system for. For the one value of lambda I get a solution, which seems alright.</p>
  
  <p>For the other value of lambda I get a solution again (matlab exits with a flag of 1. However I know this is not an actual solution For example I know that some of the dimensions of x have to be equal to each other, and this is not the case in the solution I get from fsolve.</p>
  
  <p>I have tried both trust-region and the levenberg-marquardt algorithm, and I am not getting any better results. (explicitly enforcing those x's to be the same, still seems to give solutions that are not consistent with what I would be expecting from the properties of the system)</p>
  
  <p>My question is: do the algorithms used by fsolve depend on any kind of stability of the system? Could it be that changing the parameter lambda in the second case I mention above, I make the system unstable, and could that make fsolve having a hard time to solve it correctly?</p>
  
  <p>Thank you, George</p>