Determination of the Eigenvalues using the QR-Decomposition

computes eigenvalues using QR decomposition

Description

We use the QR-decomposition to obtain the eigenvalues of a matrix. The method is iterative and builds an upper-triangular matrix. The eigenvalues appear as the diagonal terms of this upper-triangular matrix. These values are found to be in agreement with those given by the Matlab built-in function: eig. A similar program using Mathematica is available at the following link:
http://library.wolfram.com/infocenter/MathSource/6612/

• MATLAB release: MATLAB 7.0.1 (R14SP1)

[Duane Hanselman]

Here is what is in the script M-file:
A=[2., 3, 4, 5; 4, 2., 5, 6; 5, 7, 2., 7; 6, 8, 10, 2.];
M=A
for i=1:100;
    [Q,R] = qr(M);
    M=R*Q;
end
M
eig(A)

[Jackie Li]

If the matrix is near sigular or sigular, does your code work right? Thanks.

[Nikolay]

 

[Longjiang Yu]

Very excellent but maybe not work in complex eigenvalue, see the following link,
http://facstaff.unca.edu/mcmcclur/class/LinearII/presentations/html/QRAlgorithms.html