iterative method for matrix inversion

hi all iam trying to apply some iterative method to have matrix inverse the method steps are

the iterations i do is not working

AA=  [ 2 4 -3 1 0 5 -7 8;
     3 2 10 -4 -1 -6 4 1;
     9 7 3 2 0 0 -4 2;
     6 4 0 -1 -1 3 10 5;
     5 2 -3 -7 -5 4 8 -8];

   bb= [38;-20;39;-16;-30];

z0=[ 2 0 -1 2 0 0 -3 1]';
 z(:,1)=z0;
 tol=1.e-3;
 error=2*tol;
if abs(bb-AA*z0)<error    xxsol=z0;
else

    while (error>tol)
         k=1;
        for i=1:m
                 zk=z(:,k);
                   numerator= (bb(i)-(AA(i,:)*zk))*S(:,i);
                   denumerator=norm(AA(i,:),1);
                   secondterm= numerator/denumerator;
%             x= zk+ secondterm;
            x(:,i)=zk+ secondterm;
            error=abs(bb-A*x(:,i));
            if  error<tol   xxsol=x(:,i);
            else
                u=sum (x(:,i));
               z(:,i+1)= 1/m * u; 
               error=abs(bb-AA*z(:,i+1));
            end
            k=k+1;
        end

    end
end

can any body check what is wrong thanks

[Jan]

It seems like you have a reason to assume, that something is going wrong. So why don't you share the important information with the readers?

Answer 1

[Jan]

Start with applying an auto-indentation: Ctrl-A Ctrl-I. This improves the readability.

k = 1
for i = 1:m
  zk = z(:,k);
  ...
  k = k + 1;
end

could be simplified to:

for k = 1:m
  zk = z(:,k);
  ...
end

This looks fancy:

numerator= (bb(i)-(AA(i,:)*zk))*S(:,i);
denumerator=norm(AA(i,:),1);
secondterm= numerator/denumerator;

Do you mean "denominator"? Anyway, prefer simpler code:

t = (bb(i) - AA(i,:) * zk) * S(:,i) / norm(AA(i,:), 1);

If "error<tol" is reached, shouldn't the loop be left by using a break? Currently the loop is not stop in the case of success.

"error" is an important Matlab function. Do not shadow it by using the name for a variable.

In if abs(bb-AA*z0)<error, are you aware, that bb-AA*z0 is a vector? In the text of the question you find clearly, that the norm of (bb-AA*z0) is wanted. If the argument of an if command is an array, this is applied internally

if all(arg(:)) && ~isempty(arg)