Numerical Stability

This issue came up at work today, I thought ya /prog/ peeps might have some info.

So what do ya'll know about the numerical stability of rotations with, matrices, euler angles, and quaterions.

Also what do you know about the methods for interpolating rotations, and which method maintains numerical stability across the interpolation operation.

>>6
Certain algorithms are numerically unstable.  It happens most often as a result of accumulated rounding error in floating point arithmatic.  It is important to identify algorithms that do not accumulate that error.

I believe the example above is a case of one of these algorithms, quaternion interpolation does not accumulate this error while euler rotation interpolation does, and I'd like to know why....but I'm starting to think peeps on this board don't have the skills to answer a question like this.