MATLAB: Displaying the answer of Newton’s method for multiple roots

newton's method multiple roots

Hello. I'm looking for a way to display my solutions for a Newton's method. There are 4 roots in my interval.
roots=[-0.0505 1.3232 1.3636 2.3333] %initial guesses corresponding to the 4 roots.
The trouble i'm having is that the script only shows the results for first root using -0.0505, while m reaches the value 4. I don't know why it cant display the other results for m=2,3,4. What could be the problem? Thanks!
m=1;
while m<=length(roots)
    x=roots(m);  % initial guess for the root
    tol=10e-8;
    fprintf('  k        xk            fx           dfx  \n');
    for k=1:50  % iteration number
        fx=sin(x^(2))+x^(2)-2*x-0.09;
        dfx=(2*(x*cos(x^2)+x-1));
        fprintf('%3d  %12.8f  %12.8f  %12.8f \n', k,x,fx,dfx);
        x=x-fx/dfx;
        m=m+1;
        if abs(fx/dfx)<tol
            return;
        end
    end
end
RUN
k        xk            fx           dfx  
1   -0.05050505    0.01611162   -2.20201987 
2   -0.04318831    0.00010707   -2.17275307 
3   -0.04313903    0.00000000   -2.17255596

Best Answer

for k=1:50  
        fx=sin(x^(2))+x^(2)-2*x-0.09;
        dfx=(2*(x*cos(x^2)+x-1));
        fprintf('%3d  %12.8f  %12.8f  %12.8f \n', k,x,fx,dfx);
        x=x-fx/dfx;
        m=m+1;
You increase m on each iteration step.
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