  We present a model of roundoff error analysis that combines simplicity with
predictive power. Though not considering all sources of roundoff within an
algorithm, the model is related to a recursive roundoff error analysis and
therefore capable of correctly predicting stability or instability of an
algorithm. By means of nontrivial examples, such as the componentwise backward
stability analysis of Gaussian elimination with a single iterative refinement
step, we demonstrate that the model even yields quantitative backward error
bounds that show all the known problem-dependent terms (with the exception of
dimension-dependent constants, which are the weak spot of any a priori
analysis). The model can serve as a convenient tool for teaching or as a
heuristic device to discover stability results before entering a further,
detailed analysis.
