High Precision Matrix Operations - Applications?

[factotumjack]

I'm starting a project in a statistical computing course and I'd like to do it on arbitrarily high precision matrix operations.  However, I'm having trouble finding applications.

I was thinking of doing something with Kirchkoff matrices and network connectivity, but if anyone has other ideas for computational projects that could use matrix operations but suffer from roundoff error, I'd appreciate hearing about them.

Thanks
- Jack