Nonlinear overdetermined equation systems

Question

Mustafa Duran 2023-8-8

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此问题的直接链接

https://ww2.mathworks.cn/matlabcentral/answers/2006387-nonlinear-overdetermined-equation-systems

编辑： Torsten 2023-8-8

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?

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Answer 1

Torsten 2023-8-8

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https://ww2.mathworks.cn/matlabcentral/answers/2006387-nonlinear-overdetermined-equation-systems#answer_1284997

编辑：Torsten 2023-8-8

在 MATLAB Online 中打开

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