matlab index out of bounds because numel

Can you help me with this code:

function [r, niter] = fpiter(g,x0,maxiter)
i = 1;
x(1,:) = x0;
tol = 1e-05;
while i <= maxiter
   x(i+1,:) = g(x(i,:));
   if abs(x(i+1,:)-x(i,:)) < tol    %stopping criterion
      disp('The procedure was successful after k iterations')
      niter = i
      disp('The root to the equation is')
      r = x(i+1)
      return
   end
   i = i+1;
end

if abs(x(i)-x(i-1)) > tol | i > N
   disp('The procedure was unsuccessful')
   disp('Condition |p(i+1)-p(i)| < tol was not sastified')
   tol
   disp('Please, examine the sequence of iterates')
   x = x'
   disp('In case you observe convergence, then increase the maximum number of iterations')
   disp('In case of divergence, try another initial approximation p0 or rewrite g(x)')
   disp('in such a way that |g''(x)|< 1 near the root')
end

Here's the g function:

function y = g(x)
y = x.^2 - 2.*x + 1;

I got this error when I'm running it with the code: fpiter('g',1, 5)

Attempted to access g(103); index out of bounds because numel(g)=1.

Error in fpiter (line 6)
   x(i+1) = g(x(i));

Thank you :)

Answer 1

[Walter Roberson]

Run the code as

   fpiter(@g,1, 5)

[Elvin]

It worked but I don't know why it took the code to finish all the iterations and then it was unsuccesful.

Here's the result: The procedure was unsuccessful Condition p(i+1)-p(i) < tol was not sastified

tol =

     1.0000e-05

Please, examine the sequence of iterates

x =

       1
       0
       1
       0
       1
       0

In case you observe convergence, then increase the maximum number of iterations
In case of divergence, try another initial approximation p0 or rewrite g(x)
in such a way that |g'(x)|< 1 near the root

[Walter Roberson]

x = g(g(x)) when x = 0, 1, 3/2-(1/2)*5^(1/2), 3/2+(1/2)*5^(1/2)

If you start with x0 = 1/2 then you will get to your tolerance eventually, but it will take more than 5 steps, and g() of that will be close to 1 -- it will bounce around getting closer to 0 then to 1 as you go. And if your x0 is 3 then every step will increase in value and no root will be found.

[Elvin]

May I know what would be the "fix" that I could do to this could? By the way, here's what I'm trying to do: http://i.minus.com/inFVYTNmwZZh9.PNG

[Walter Roberson]

Your routine does do fixed-point iteration. However, it happens that for every quadratic that does not happen to have a certain specific relationship of coefficients, that there are two fixed point values, x = g(x), and two more fixed point values, x = g(g(x)), and four more fixed point values x = g(g(g(x))) . Some of these roots are likely to be imaginary.

In any case, as you are looking for roots of the polynomial, you should be adding the check g(x) == 0, because no matter whether the difference between x and g(x) is less than the tolerance, if g(x) is 0 then x is a root.

[Elvin]

I've tried to change my answer to this:

      function [r,niter,x] = fpiter(g,x0,maxiter)
      x(1) = x0;
      tol = 0.50;
      for niter=1:maxiter
          x(niter+1) = g(x(niter));
          eval=feval(g,x(niter));
          if (abs(x(niter+1)-x(niter))<=tol)|(eval==0)
              break
          end
      end
      x;
      r=x(niter);

but I can't solve a quadratic equation. Can you help me change my code? Thanks