Limitations of Backward Error Analysis
Dr. Sanzheng Qiao
Dr. David Parnas
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.