Newton's method(calculating the angel)

%% 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?

[John D'Errico]

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]

how do i fix that?

Answer 1

[Sriram Tadavarty]

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