why is my Fixed point iteration method only giving me first iteration. (i included info at the bottom of code and the next few iterations answers)

x= sym('x');

tol=.00001;

n_0=input('Plese input your number of iterations: ');

p_0=input('Plese input your initial approximation: ');

F = input('Plese input your equation: ');

%g = (10/(4+x))^(1/2);

N=0;

p=(subs(F,x,p_0));

while(N <= n_0 && not(abs(p-p_0) <= tol ))

N=N+1;

F=p;

p_0=p;

display(double(p_0))

end

% iterations= 30

% initial approxiation= 1.5

% equation= (10/(4+x))^(1/2)

% iterations: 1.5, 1.348399725, 1.367376372, 1.364957015, 1.365264748, ...

[Dimitris Kalogiros]

What do you intend to achieve with this code?

What is the goal ? Solving an equation? which is the equation ?

Answer 1

[John D'Errico]

Think about it. Does p EVER change? Why not? How would you make it change?

Inside the loop, we see only this:

N=N+1;
F=p;
p_0=p;
   
display(double(p_0))

p starts out as whatever number is it. Does it EVER change? (NO.)

When you do this:

F=p;

Here, I think you think this evaluates the FUNCTION every time. It does not. p is a number. It sets F to be the number p.

Therefore, p_0 = p. ALWAYS. Now, what does your test do? It terminates the loop when p0-p is a small enough number. Zero certainly satisfies the requirement. So the loop runs for one iteration, then quits.

So, change your code to re-evaluate the function inside F. Do not overwrite the variable F.

[Erik Ramirez]

Thank you so much!!!