function [lambda,V,k]=invpowerm(A,X,alpha,epsilon,max1)

%Input    - A is an nxn matrix
%            - X is the nx1 starting vector
%            - alpha is the given shift
%            - epsilon is the tolerance
%            - max1 is the maximum number of iterations
%Output - lambda is the dominant eigenvalue
%            - V is the dominant eigenvector
%            - k is the number of iteration

%  NUMERICAL METHODS: Matlab Programs
% (c) 2007 by Xie Liling
%  Complementary Software to accompany the textbook:
%  Information and Computing Science: A Laboratory Course

%Initialize the matrix A-alpha*I and parameters
[n n]=size(A);
A=A-alpha*eye(n);
lambda(1)=0;
err=1;
k=1;

while ((k<=max1)&(err>epsilon))
   %Solve system AY=X
   Y=A\X;
   
   %Normalize Y
   m=max(abs(Y));
   dc=abs(lambda-m);
   Y=(1/m)*Y;
   
   %Update X and lambda and check for convergence
   dv=norm(X-Y);
   err=max(dc,dv);
   X=Y;
   k=k+1;
   lambda(k)=m;
end

k=k-1;
lambda(end)=alpha+1/m;
V=X;