power.m

sareli<matlab科学计算>配套程序

function [lambda,x,iter]=power(A,tol,nmax,x0)
%POWER     Numerically evaluate one eigenvalue of a matrix.
%   LAMBDA = POWER(A) compute with the power method the 
%   eigenvalue of A of maximum modulus.
%   LAMBDA = POWER(A,TOL,NMAX,X0) uses an absolute error tolerance of TOL 
%   instead of the default, which is 1.e-6 and a maximum number of iterations
%   of NMAX (the default is 100), starting from the initial vector X0.
%   [LAMBDA,V,ITER] = POWER(A,TOL,NMAX,X0) also returns the eigenvector
%   V such that A*V=LAMBDA*V and the iteration number at which V was computed.
[n,m] = size(A);
if n ~= m, error('Only for square matrices'); end

nargin
if nargin == 1
   tol = 1.e-06;
   x0 = ones(n,1);
   nmax = 100;
end   
x0 = x0/norm(x0); 
pro = A*x0; 
lambda = x0'*pro;
err = tol + 1; 
iter = 0
while err > tol*abs(lambda) & abs(lambda) ~= 0 & iter <= nmax
   x = pro; x = x/norm(x); 
   pro = A*x; lambdanew = x'*pro;
   err = abs(lambdanew - lambda); 
   lambda = lambdanew;
   iter = iter + 1;
end