Newton's method(calculating the angel)

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Ahmed Alhawaj
Ahmed Alhawaj on 15 Mar 2020
Answered: Sriram Tadavarty on 16 Mar 2020
%% 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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Answers (1)

Sriram Tadavarty
Sriram Tadavarty on 16 Mar 2020
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
This will fix the loop operation.
Hope this helps.
Regards,
Sriram

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