Solution is going to infinite iterations

I am getting infinite iterations, please help me.

clear all
a=0.5;
err=1e-6;
count=0;
x=100;
%fx = a-cos(a);
%dfx= 1+sin(a);
%x1=a-(fx/dfx);
while abs(a-x)>err
    fx=x-cos(x);
    dfx= 1+sin(x);
    x1=x-(fx/dfx);
    %x=abs(x1-x);
    %x=x1;
    if abs(x1-a)>err
        x=x1;
  %elseif abs(a-x1)>err
   %     continue
     end
    count = count + 1;
    sprintf('After iteration %2.0d the x is %3.15f',count,x)
end

Answer 1

[Torsten]

Your decision variable in the while statement must be

abs(fx)> err

and/or

abs(x1-x)>err

but not

abs(x1-a)>err

Note that 0.5 is not a root of f(x)=x-cos(x).

Best wishes

Torsten.

[Shripad]

Thanks for the help Torsten, your first suggestion (abs(fx)> err ) worked for me. But with your second suggestion (abs(x1-x)>err),which I thought to be more logical, MATLAB was performing only one iteration. Kindly help me to resolve this issue.

Thanks again.

[Torsten]

After the commands in the while-loop have been executed, MATLAB checks the exit condition and exits if they are no longer true. Since you set x=x1 at the end of the while-loop, the condition to exit (abs(x-x1)<=err) will be satisfied after the first iteration. The remedy is to set x=x1 at the start of the while-loop.

Best wishes

Torsten.