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 $A,Q$.

$Q^t$$A$$Q$$B$
1.000.000.000.000.00
0.001.000.000.000.00
0.000.001.000.000.00
0.000.000.001.000.00
0.000.000.000.001.00
*****
*****
*****
*****
*****
1.000.000.000.000.00
0.001.000.000.000.00
0.000.001.000.000.00
0.000.000.001.000.00
0.000.000.000.001.00
=
*****
*****
*****
*****
*****
$\sum_{i\neq j}a_{ij}^2=$* $c=$
$\sum_{i}a_{ii}^2=$* $s=$



Copyright by © Gábor P. Nagy, 2013.