I am looking for a Java-based numerical method package that provides functionality including:

- Solving systems of equations using different numerical analysis algorithms.
- Matrix methods (e.g., inversion).
- Spline approximations.
- Probability distributions and statistical methods.

In this case, "best" is defined as a package with a mature and usable API, solid performance and numerical accuracy.

Edit: derick van brought up a good point in that cost is a factor. I am heavily biased in favor of free packages but others may have a different emphasis.