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

% shifted inverse LU decomposition of the matrix A, where the matrix P is
% a permutation matrix corresponding to the pivoting strategy 
% used.
A = [1 3 7; 2 -4 5; 3 4 -6]
B = A+6*eye(3)
C = inv(B)
x = [1; 1; 1]
for k=1:30
  y = C*x;
  r = y(2)/x(2)
  x = y/norm(y)
end