Why doesnt e1 converges to zero

this my code for the power irritation

% A is the Student Matrix after adding the three students

clear all

A = load('student_adjacency.txt');

[b, eval]=eigs(A,1);

k=1;

b0 = rand(30,1);

e1 = 1;

while e1 > 10E-6

      b1 = (A*b0)/norm(A*b0);

      e0=norm((b0-b));

      e1=norm((b1-b))

      r=e1/e0;

      b0 = b1;

      k=k+1;
  end

so why don't e1 go to zero

[Image Analyst]

http://www.mathworks.com/matlabcentral/answers/13205-tutorial-how-to-format-your-question-with-markup

Answer 1

[Roger Stafford]

Eigenvectors are not uniquely determined even if normalized. For real-valued vectors they may be either of two opposite directions. For complex-valued vectors they can differ by any arbitrary complex factor of magnitude 1. Thus, your algorithm may not converge to the particular 'b' which 'eigs' has returned. It depends on the random vector you start with. For the real-valued case I would say your odds of success are about 50-50.