Limitations of Backward Error Analysis


Dr. Sanzheng Qiao

and

Dr. David Parnas


Abstract

We know that a small backward error given by a backward error analysis of a numerical method ensures the stability of the method. In this paper, we show, through examples, that a large backward error or non-existence of backward error does not imply instability. In fact, a method can be stable and deliver accurate results although the backward error is large.