  Numerical Analysts and scientists working in applications often observe that
once they improve their techniques to get a better accuracy, some instability
creeps in through the back door. This paper shows for a large class of
numerical methods that such a Trade-off Principle between error and stability
is unavoidable. The setting is confined to recovery of functions from data, but
it includes solving differential equations by writing such methods as a
recovery of functions under constraints imposed by differential operators and
boundary values. It is shown in particular that Kansa's Unsymmetric Collocation
Method sacrifices accuracy for stability, when compared to symmetric
collocation.
