Nonlinear overdetermined equation systems

There is a nonlinear overdetermined system. For example:

syms x y z t
x+y+z+t=0.5
3x+4y+5z+2t=5
2x+9y+3z+4t=6
2x+4y+8z+6t=2
x^2+y^2+3z+6t=9

I found the solution for linear overdetermined systems. However how can i solve nonlinear overdetermined equation systems like that in MATLAB?

Answer 1

[Torsten]

By using "lsqnonlin", e.g.

sol0 = [0 0 0 0];
sol = lsqnonlin(@fun,sol0)

Local minimum possible.

lsqnonlin stopped because the final change in the sum of squares relative to 
its initial value is less than the value of the function tolerance.

sol = 1×4

2.7023 0.0552 -1.0198 0.7598

norm(fun(sol))

ans = 2.0264

function res = fun(u);
  x = u(1);
  y = u(2);
  z = u(3);
  t = u(4);
  res = [x+y+z+t-0.5,...
         3*x+4*y+5*z+2*t-5,...
         2*x+9*y+3*z+4*t-6,...
         2*x+4*y+8*z+6*t-2,...
         x^2+y^2+3*z+6*t-9];
end