What is causing this to have an infinite loop??

%testing our newton's method on a known problem
%we know the root is pi
p0 = 1;%initial guess
tol = 1e-8;
exact = 3.14159;%exact root
%enter function and its derivative
f = @(x) sin(x);
fp = @(x) cos(x);
%compare initial guess to exact root
diff = abs(p0-exact);
%iterate newton's method
while diff > tol
    p = p0 - f(p0)/fp(p0);
    diff = abs(p-exact); %stop when our iterate is close to the exact root, pi
    p0 = p;
end
%print the root to the screen
p

[KL]

If you have access to symbolic math toolbox, I'd suggest vpa/digits.

https://www.mathworks.com/help/symbolic/vpa.html https://www.mathworks.com/help/symbolic/digits.html

[Guillaume]

Completely unrelated to the problem: it is not a good idea to name a variable diff as it will prevent you from using the very useful diff function.

Answer 1

[Birdman]

Add a condition to break out of the loop then the while condition is not satisfied as:

while diff > tol
    if ismembertol(diff,exact,tol)
       break;
    end
    p = p0 - f(p0)/fp(p0);
    diff = abs(p-exact); %stop when our iterate is close to the exact root, pi      
    p0 = p;
end

[Phi Tran]

Why wouldn't the loop above work though? Why does it need a break?

[Birdman]

Because when I printed diff, it converges to 3.1416 but your tol variable is 1e-8. Since 3.1416 is greater than 1e-8, it will not leave the while loop. You need to break it manually and you did not give any condition to break your loop.

[Torsten]

Just print the p-values.

My guess is that p->0, not ->pi.

Best wishes

Torsten.

[Phi Tran]

thanks