[Solved] Power method, eigenvalues.
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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?
7 Comments
Lorenzo Amabili
on 17 Mar 2017
Edited: Lorenzo Amabili
on 17 Mar 2017
@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!
Accepted Answer
Teja Muppirala
on 13 May 2011
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)
More Answers (3)
Andrew Newell
on 12 May 2011
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;
2 Comments
devalaraju venkata naga amulya
on 24 Jul 2019
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
on 28 Aug 2020
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.
Akankshya
on 13 Feb 2024
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
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