Re: Which algorithm does Octave use to invert the following positive semidefinite matrix?

[Martin Helm]

Am Montag, 4. April 2011, 16:45:28 schrieb Olumide:
> Can someone tell me what algorithm Octave uses to invert the following
> positive semidefinite matrix, that has zeros along its diagonal.
> Matrices of this sort that arise in scattered data interpolation with
> radial basis functions.
> 
> [     0.000000   529.831737  1198.292909   529.831737     1.000000
> 10.000000     0.000000 ]
> [   529.831737     0.000000   529.831737  1198.292909     1.000000
> 0.000000    10.000000 ]
> [  1198.292909   529.831737     0.000000   529.831737     1.000000
> -10.000000     0.000000 ]
> [   529.831737  1198.292909   529.831737     0.000000     1.000000
> 0.000000   -10.000000 ]
> [     1.000000     1.000000     1.000000     1.000000     0.000000
> 0.000000     0.000000 ]
> [    10.000000     0.000000   -10.000000     0.000000     0.000000
> 0.000000     0.000000 ]
> [     0.000000    10.000000     0.000000   -10.000000     0.000000
> 0.000000     0.000000 ]
> 
> Whereas the LAPACK routines DPOTRI and DGETRI fail because the matrix
> has zero elements along its diagonal, Octave successfully computes
> the inverts the matrix to be
> 
> [  1.8034e-003  -1.8034e-003   1.8034e-003  -1.8034e-003   2.5000e-001
>   5.0000e-002  -2.2854e-018 ]
> [ -1.8034e-003   1.8034e-003  -1.8034e-003   1.8034e-003   2.5000e-001
> -1.4014e-017   5.0000e-002 ]
> [  1.8034e-003  -1.8034e-003   1.8034e-003  -1.8034e-003   2.5000e-001
> -5.0000e-002  -1.1356e-017 ]
> [ -1.8034e-003   1.8034e-003  -1.8034e-003   1.8034e-003   2.5000e-001
> -1.2975e-017  -5.0000e-002 ]
> [  2.5000e-001   2.5000e-001   2.5000e-001   2.5000e-001  -5.6449e+002
>   1.6031e-015  -2.2001e-015 ]
> [  5.0000e-002   1.5053e-017  -5.0000e-002   1.1470e-017  -1.6031e-015
>   5.9915e+000   2.3211e-016 ]
> [  1.3878e-017   5.0000e-002   5.8566e-018  -5.0000e-002   1.4668e-015
> -1.6985e-017   5.9915e+000 ]
> 
> I've verified that the product of both matrices is the identify
> matrix.
> 
> Thanks,
> 
> - Olumide
> 
Just one question: Why do you think your matrix is positiv semidefinite? It has 
positive and negative eigen values!