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Determination of the Eigenvalues using the QR-Decomposition

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computes eigenvalues using QR decomposition

Updated 31 Jan 2007

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/

Cite As

Housam Binous (2021). Determination of the Eigenvalues using the QR-Decomposition (https://www.mathworks.com/matlabcentral/fileexchange/13813-determination-of-the-eigenvalues-using-the-qr-decomposition), MATLAB Central File Exchange. Retrieved .

Aras

Ashutosh kumar

This code is not giving correct result for this matrix:
A=[1, 1, 0; 1, 0, 1; 0, 1, 1]
can someone please tell me why?

Jan

I recommend not to download this piece of code, because it is neither useful nor usable. "[Q,R]=qr(M); M=R*Q;" is calculated 100 times. This is *not* a smart method to determine eigenvalues reliably.

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

Nikolay

Jackie Li

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

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)

MATLAB Release Compatibility
Created with R14SP1
Compatible with any release
Platform Compatibility
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