How to plot a graph of convergence for Newtons method of three variables?

Question

Marcus 2014-12-31

0
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此问题的直接链接

https://ww2.mathworks.cn/matlabcentral/answers/168611-how-to-plot-a-graph-of-convergence-for-newtons-method-of-three-variables

回答： Zoltán Csáti 2014-12-31

Hi, I have used Newtons method to find three unknown variables from three equations, but now I need to plot the graph to show the convergence and I'm not really sure how to do so. My code for Newtons method is below:

function g = uppgift12(L3, m1, m2)
u=[pi/4 0 -pi/4]';
iter=0;, dunorm=1;
while dunorm>0.5e-4 & iter<10
 f=[cos(u(1))+cos(u(2))+L3*cos(u(3))-2
    sin(u(1))+sin(u(2))+L3*sin(u(3))
  m2*tan(u(1))-(m1+m2)*tan(u(2))+m1*tan(u(3))];
 J=[-sin(u(1)) -sin(u(2)) -L3*sin(u(3))
    cos(u(1)) cos(u(2)) L3*cos(u(3))
  m2*sec(u(1))^2 -m1*sec(u(2))^2-m2*sec(u(2))^2 m1*sec(u(3))^2];
 du=-J\f;
 u=u+du;
 dunorm=norm(du,inf);, iter=iter+1;
end
u, iter;

The variables are u(1), u(2), u(3). The variables L3, m1, m2 are given in four different parameters, (1,1,1), (1,1,2), (2,1,1) and (1,10,1) and I have to show the plots of convergence for all three variables of u for all four parameters. I really appreciate any response, thanks for your help.

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Answer 1

Zoltán Csáti 2014-12-31

0
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此回答的直接链接

https://ww2.mathworks.cn/matlabcentral/answers/168611-how-to-plot-a-graph-of-convergence-for-newtons-method-of-three-variables#answer_163740

This is a classic parameter sweep. Alter one parameter while the others are fixed. Then solve the nonlinear equations. When you want to plot the convergence, you can do it as follows. On the horizontal axis, plot the iteration number. On the vertical axis, display the function value difference (in some norm) between the current and the former iteration.