Eigenvalue Problem for symmetric matrices: The Jacobi Method

For the mathematical background, please read the Wikipedia page on the Jacobi method.

The parameters

Matrix dimension = 5. Precision = 2 digits. Magnitude of matrix entries = 100.

The diagonalization

1. Determine $i,j$ ($i\neq j$) such that $|a_{ij}|$ is maximal.
2. Compute $c,s$.
3. Recalculate $\Lambda,Q$.

$Q$ $\Lambda$ $Q^T$ $A$
1.00 0.00 0.00 0.00 0.00
0.00 1.00 0.00 0.00 0.00
0.00 0.00 1.00 0.00 0.00
0.00 0.00 0.00 1.00 0.00
0.00 0.00 0.00 0.00 1.00
* * * * *
* * * * *
* * * * *
* * * * *
* * * * *
1.00 0.00 0.00 0.00 0.00
0.00 1.00 0.00 0.00 0.00
0.00 0.00 1.00 0.00 0.00
0.00 0.00 0.00 1.00 0.00
0.00 0.00 0.00 0.00 1.00
=
* * * * *
* * * * *
* * * * *
* * * * *
* * * * *
$c=$ $s=$
$\mathrm{sqsum}(\Lambda)=$* $\mathrm{diagss}(\Lambda)=$* diff =* 


	

	
Copyright by © Gábor P. Nagy, 2013.