Hello Jason_S,
If you double click subVI, you can view its block diagram. If you do this for Inverse Matrix.vi, then select the "Positive Definite" case in the case structure, you will see that it calls a subVI called Real Inverse Matrix (Cholesky).vi. This would suggest that the Cholesky Decomposition algorithm is the one that is used. However, since Real Inverse Matrix (Cholesky).vi calls a library function, you cannot determine the exact algorithm that is used.
Wan L
Applications Engineer
National Instruments
http://www.ni.com/support