# How to solve a nonlinear system of n equations

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Joseph El Bacha on 14 Oct 2014
Answered: Alex Sha on 11 Dec 2019
Hi, I solved a nonlinear system of n equations using fsolve and it succeeded. But I couldnt solve another nonlinear system using fsolve. In fact it worked but its giving me wrong answers. I sent an email to mathworks but had no reply. Can Anyone help plz ?
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Joseph El Bacha on 14 Oct 2014
Please find 2 M.files as attachments trying to resume my whole problem. I have a catalog of the right answers and Im sure my system is giving me wrong answers. The right vector for the files I uploaded is (42.00 60.00 78.00).
P.S: I can get this result if I insert it as an initial vector. But I dont want to do that.

Alan Weiss on 14 Oct 2014
Your function is not smooth--it has both abs and sign calls. Therefore you cannot expect fsolve to work effectively starting from every point.
For more help, see fsolve could not solve the equation, which basically says that for this kind of problem you have to start from a wide variety of points.
Good luck,
Alan Weiss
MATLAB mathematical toolbox documentation
Joseph El Bacha on 14 Oct 2014
I already tried different initial points but it is not working unless I am 10^-5 close to the right answer.
How am I supposed to solve it through MATLAB if fsolve cannot help ?

Matt J on 14 Oct 2014
Edited: Matt J on 14 Oct 2014
In view of how difficult your equations are, and because there are only 3 unknowns, I would just use exhaustive search, but in a multiresolution way. Start by sampling F(x1,x2,x3) on a coarse grid,e.g. with
[x1,x2,x3]=ndgrid(0:.1:10);
Evaluate F at all points on this grid (using vectorization, of course) and use min() to find the least norm(F) over all points. Then create a finer grid in the near neighborhood of the approximate solution and repeat...

Alex Sha on 11 Dec 2019
some results:
1:
x1: 1.04727193704753
x2: 2.09481403258296
x3: -3.14176920919256
2:
x1: -1.04719783053703
x2: 4.76397520013691E-7
x3: 1.04719557784678
3:
x1: -1.04722327842385
x2: -1.0469722124015
x3: 3.14151227631221