invpow.m

来自「数值计算方法的教程」· M 代码 · 共 53 行

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) 2004 by John H. Mathews and Kurtis D. Fink
%  Complementary Software to accompany the textbook:
%  NUMERICAL METHODS: Using Matlab, Fourth Edition
%  ISBN: 0-13-065248-2
%  Prentice-Hall Pub. Inc.
%  One Lake Street
%  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=Y(j);
   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;