% Numerical Mathematics and Computing, Fifth Edition
% Ward Cheney & David Kincaid
% Brooks/Cole Publ. Co.
% (c) 2003
%
% file: small_eig.m

% compute smallest eigenvalue/eigenvector via inverse power method
% 
A = (1/3)*[-155 528 407; 55 -144 -121; -132 396 318]
B = inv(A)
x = [1; 2; 3]
for k=1:80
  y = B*x;
  r(k) = x(2)/y(2)
  x = y/norm(y, inf);
end
for k=3:80
  s(k) = (r(k-2)*r(k)-r(k-1)^2)/(r(k)-2*r(k-1)+r(k-2))
end
format long
r(80), s(80), x, A*x, s(80)*x