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## Which algorithm does Octave use to invert the following positive semidef

 From: Olumide Subject: Which algorithm does Octave use to invert the following positive semidefinite matrix? Date: Mon, 04 Apr 2011 15:45:28 +0100 User-agent: Mozilla/5.0 (Windows; U; Windows NT 5.1; en-US; rv:1.9.2.15) Gecko/20110303 Thunderbird/3.1.9

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

```