2. A stochastic approach to rounding error analysis: the CESTAC method

The methods presented above can be used to estimate major bounds on the propagation of rounding errors or on the intervals in which the exact solution of the problem under study can be found, and to estimate the stability of the algorithms used.

Since the advent of computers capable of executing billions of operations per second, users have become increasingly aware of the need to know the reliability of the results provided by the computer after several hours of arithmetic calculations performed with floating-point arithmetic and, often, with data tainted by uncertainties. Only the stochastic approach is capable of providing an answer.