1. Estimating the influence of rounding errors and data uncertainties

When a scientific program is run on a computer, calculations are performed in floating-point arithmetic, using data that is generally subject either to rounding errors (errors due to the assignment operator), or to uncertainties due to physical measuring devices (sensors).

The results provided by the computer are therefore always tainted by errors resulting from the propagation of rounding errors and the influence of data uncertainties. It is therefore always necessary to estimate here, and not to overestimate, the influence of these errors on all the results of the program and, therefore, of the algorithm implemented.

Let