[Solved] Power method, eigenvalues.

function l = ww(A,E)

n = length(A);
y = [];

x = [];
for i = 1:n            % starting vector
    x(i) = A(i,1);
end;

l = 0;
blad = E;        % starting value of error
while blad>=E

      for i = 1:n    % A*x
          y(i) = 0;
          for j = 1:n
              y(i) = y(i) + A(i,j)*x(j);
          end;
      end;

      blad = l;

      l = 0;           % Rayleigh
      m = 0;
      for i = 1:n
          l = l + x(i)*y(i);
          m = m + x(i)*x(i);
      end;
      l = l/m;           % eigenvalue
      blad = abs(l - blad);         % error
      x = y;
  end;

end

That's how I've tried to compute eigenvalues. It works for some matrices, but for:

A =

           0   -0.3333   -0.3333
     -0.3333         0    0.3333
      0.6000    0.2000         0

it doesn't work. How can I fix that?

[Walter Roberson]

What difference do you see between what you expect and what is output?

[Matt Fig]

And what is the input E??

[John D'Errico]

Wow. Looks just like Fortran code to me.

[Andrew Newell]

Fortran 77; 90 has vector operations.

[Kamil]

@ Matt Fig

E - error of approximation.

[Lorenzo Amabili]

@Kamil

@Teja Muppirala

how do you set E initially? I am sorry in case this question is silly but I am still new to this field. Thank you!

[karim hamza]

i have an error [not enough input argument]

Answer 1

[Teja Muppirala]

Simple power iteration only works when there is a single dominant eigenvalue. The matrix

A =[  0        -0.3333   -0.3333
     -0.3333         0    0.3333
      0.6000    0.2000         0];

has 3 eigenvalues,

-0.3333          
 0.1667 + 0.3249i
 0.1667 - 0.3249i

with absolute values:

    0.3333
    0.3651
    0.3651

As you can see, the dominant eigenvalue is not unique. That is why your algorithm fails to converge.

One way to fix this is by using shifts (you can read all about it on Google).

But why not just use MATLAB's built in eigevnalue solver, EIG?

eig(A)

[Kamil]

Thank you, I forgot about that.

I didn't use EIG, because I'm studying Numerical Methods and I'm trying to exercise that way.

Answer 2

[Andrew Newell]

While we wait for more information, here is a vectorized version of whatever your algorithm is doing:

function l = ww(A,E)

x = A(:,1);

l = 0;
blad = E;        % starting value of error
while blad>=E

    y = A*x;

    blad = l;

    l = x.*y;  % Rayleigh
    m = x.*x;

    l = l/m;           % eigenvalue
    blad = abs(l - blad);         % error
    x = y;
end;

[devalaraju venkata naga amulya]

when i run the above code there is an error of input values A and E(in line function) can u help it with me im sorry im very new to the matlab

[Dhruv Bhavsar]

Try calling the function in the command prompt even if you get the above mentioned error.

If it works then copy the function at the bottom of a new script and write the codes to be implemented above the function defined.

I have attached my code file for your reference.

Answer 3

[Kamil]

Are there any other methods of computing eigenvalues?

Answer 4

[Akankshya]

function l = ww(A,E)

x = A(:,1);

l = 0;

blad = E; % starting value of error

while blad>=E

y = A*x;

blad = l;

l = x.*y; % Rayleigh

m = x.*x;

l = l/m; % eigenvalue

blad = abs(l - blad); % error

x = y;

end