Newton's method(calculating the angel)

Question

Ahmed Alhawaj 2020-3-15

0
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此问题的直接链接

https://ww2.mathworks.cn/matlabcentral/answers/511009-newton-s-method-calculating-the-angel

回答： Sriram Tadavarty 2020-3-16

%% Newton's method

w = 30; h = 30; c = 3.5; % In inches

f = @(theta) w*sind(theta) - h*cosd(theta) - c;

fp = @(theta) w*cosd(theta)+h*sind(theta);

theta_newt(1) = 49.49; % Set initial guess

tol=0.4771;

n=1;

while n==1:50

fe = f(theta_newt(1));

fpe = fp(theta_newt(1));

theta_newt(n+1) = theta_newt(n) - fe(n)/fpe(n);

if theta_newt(n+1)>= 49.73-tol || theta_newt(n+1)< 49.73+tol

theta=theta_newt(n+1);

break

end

n = n + 1;

end

I am trying to run this code but it seems that the loop isnt working properly

how would I fix that?

Also,How would I show how many iteration it takes to come up with the wanted angle?

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John D'Errico 2020-3-15

编辑：John D'Errico 2020-3-15

在 MATLAB Online 中打开

Why are you using Newton's method anyway? Why not use fzero? Never write your own solver code.

That you should not be writing your own solvers is evidenced by you use of non-working constructs. For example:

while n==1:50

That is not how you construct a while loop.

Ahmed Alhawaj 2020-3-15

how do i fix that?

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Answer 1

Sriram Tadavarty 2020-3-16

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链接

此回答的直接链接

https://ww2.mathworks.cn/matlabcentral/answers/511009-newton-s-method-calculating-the-angel#answer_420273

Hi Ahmed,

To make the code working, perform the following changes:

Update the while loop with proper condition
Calculate fe and fpe for each n
Do not access the fe and fpe with indexing variable, since it is a scalar

This leads to following update in the while loop

 while n <= 50 % Proper loop condition
  fe = f(theta_newt(n)); % Calculate for each n
  fpe = fp(theta_newt(n)); % Calculate for each n
  theta_newt(n+1) = theta_newt(n) - fe/fpe; % Remove the indexing here
  if theta_newt(n+1)>= 49.73-tol || theta_newt(n+1)< 49.73+tol
    theta=theta_newt(n+1); 
    break
  end
  n = n + 1;
 end