qr1.m

关于数值计算的matlab程序代码,包含了很多的实用的算法.程序全部可以直接用的,有详细的英文注释.

function D=qr1(A,epsilon)

%Input - A is a symmetric tridiagona nxn matrix
%      - epsilon is the tolerance
%Output - D is the vector of eigenvalues

%  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 parameters

[n,n]=size(A);
m=n;

while (m>1)
   S=A(m-1:m,m-1:m);
   if abs(S(2,1))<epsilon
      A(m,m-1)=0;
      A(m-1,m)=0;
    
   else
      shift=eig(S);
      [j,k]=min([abs(A(m,m)-shift(1)) abs(A(m,m)-shift(2))]);
   end
   [Q,U]=qr(A-shift(k)*eye(n));
   A=U*Q+shift(k)*eye(n);
   m=m-1;
end

D=diag(A);