[lambda,V]=invpow(A,X,alpha,epsilon,max1)

function [lambda,V]=invpow(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

% NUMERICAL METHODS: MATLAB Programs
%(c) 1999 by John H. Mathews and Kurtis D. Fink
%To accompany the textbook:
%NUMERICAL METHODS Using MATLAB,
%by John H. Mathews and Kurtis D. Fink
%ISBN 0-13-270042-5, (c) 1999
%PRENTICE HALL, INC.
%Upper Saddle River, NJ 07458

%Initialize the matrix A-alphaI and parameters

[n n]=size(A);
A=A-alpha*eye(n);
lambda=0;
cnt=0;
err=1;
state=1;

while ((cnt<=max1)&(state==1))
   
   %Solve system AY=X
   Y=A\X;
   
   %Normalize Y
   [m j]=max(abs(Y));
   c1=m;
   dc=abs(lambda-c1);
   Y=(1/c1)*Y;
   
   %Update X and lambda and check for convergence
   dv=norm(X-Y);
   err=max(dc,dv);
   X=Y;
   lambda=c1;
   state=0;
   if (err>epsilon)
      state=1;
   end
   cnt=cnt+1;
end

lambda=alpha+1/c1;
V=X;