Numerical analysis has a useful cast of recurring examples. Some are famous because a perfectly innocent formula becomes ill conditioned. Some expose cancellation, instability, locality, or the consequences of a bad starting value. A few are simply very good at making an algorithm admit what it was assuming all along.
The entries here are worked problems rather than dictionary definitions. Each one starts with the object, works far enough by hand to identify the mechanism, gives R code, and points into the CMNA laboratories where the problem can be pushed around.