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

[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