Computer Search for Numerical Instability

ABSTRac~r. It is often possible to define a measure, ~(d) ~ 0, of the effect of rounding error upon a fixed numerical algorithm given data d. One reasonable choice is for ~ to measure how much the exact computational problem must be perturbed to compensate for rounding error. In this paper such "Wilkinson numbers" ~(d) are investigated, with particular attentmn given to their numerical evaluation Also, an automatic roundoff analysis m described, which shows that the usual algorithm for inverting triangular matrices does not enjoy a certain very stringent stabdlty property