Graphs and stability of algorithms

Abstract:

In this paper the method of [22] for roundoff error analysis is extended to the relative case. Two statements are proved for the analysis of backward stability and two corresponding classes of backward stable algorithms are characterized in a constructive way. The error bounds obtained with this approach rely on properties of dependence graphs and are of remarkable generality. A first-order error analysis is provided even though the terms of higher order in the error bounds can be easily estimated. Some examples of the application of the new technique are given in which either we obtain new error bounds or we derive known results in a new way.