Power Method Algorithm using MATLAB(m-file)

Finding eigenvalue and eigenvector

MATLAB Program:

% Power Method Algorithm

 n=input('Enter dimension of the matrix, n:  ');

 A = zeros(n,n);

 x = zeros(1,n);

 y = zeros(1,n);

 tol = input('Enter the tolerance, tol: ');

 m = input('Enter maximum number of iterations, m:  ');

 A=[1 2 0; -2 1 2; 1 3 1];

 x=[1 1 1];

 k = 1; lp = 1;

 amax = abs(x(1));

 for i = 2 : n

    if abs(x(i)) > amax

        amax = abs(x(i));

        lp = i;

    end

 end 

 for i = 1 : n

    x(i) = x(i)/amax;

  end 

 fprintf('\n\n  Ite.    Eigenvalue     ............Eigenvectores............\n');

 while k <= m 

      for i = 1 : n

         y(i) = 0;

         for j = 1 : n

           y(i) = y(i) + A(i,j) * x(j);

         end

      end

      ymu = y(lp);

      lp = 1;

      amax = abs(y(1));

      for i = 2 : n

         if abs(y(i)) > amax

            amax = abs(y(i));

            lp = i;

         end

      end

      if amax <= 0

         fprintf('0 eigenvalue - select another ');

         fprintf('initial vector and begin again\n');

      else

           err = 0;

           for i = 1 : n

              t = y(i)/y(lp);

              if abs(x(i)-t) > err

                err = abs(x(i)-t);

              end

              x(i) = t;

           end

           fprintf('%4d     %11.8f', k, ymu);

           for i = 1 : n

             fprintf('   %11.8f', x(i));

           end

           fprintf('\n');

           if err <= tol

              fprintf('\n\nThe eigenvalue after %d iterations is: %11.8f \n',k, ymu);

              fprintf('The corresponding eigenvector is: \n');

              for i = 1 : n

                 fprintf('                                 %11.8f \n', x(i));

              end

              fprintf('\n');

              break;

           end

           k = k+1;

       end

 end

 if k > m

 fprintf('Method did not converge within %d iterations\n', m);

 end

OUTPUTS:

>> power_C
Enter dimension of the matrix, n:  3
Enter the tolerance, tol: 0.00001
Enter maximum number of iterations, m:  100


  Ite.    Eigenvalue     ............Eigenvectores............
   1      3.00000000    0.60000000    0.20000000    1.00000000
   2      2.20000000    0.45454545    0.45454545    1.00000000
   3      2.81818182    0.48387097    0.54838710    1.00000000
   4      3.12903226    0.50515464    0.50515464    1.00000000
   5      3.02061856    0.50170648    0.49488055    1.00000000
   6      2.98634812    0.49942857    0.49942857    1.00000000
   7      2.99771429    0.49980938    0.50057186    1.00000000
   8      3.00152497    0.50006351    0.50006351    1.00000000
   9      3.00025403    0.50002117    0.49993650    1.00000000
  10      2.99983066    0.49999294    0.49999294    1.00000000

  11      2.99997177    0.49999765    0.50000706    1.00000000
  12      3.00001882    0.50000078    0.50000078    1.00000000


The eigenvalue after 12 iterations is:  3.00001882 
The corresponding eigenvector is: 
                                  0.50000078 
                                  0.50000078 

                                  1.00000000