Validating the results obtained from scientific software. Stochastic approach

The following chapters are devoted to a stochastic approach to the propagation of rounding errors and the influence of data uncertainties on the results delivered by a scientific program.

This is the only method that enables every engineer to answer the question posed above, which in essence is: "What is the exact number of significant decimal places in the results provided by a scientific calculation program?"

The CESTAC method (Control and Stochastic Estimation of Computational Rounding) is detailed in Chapter 2, followed by a presentation of stochastic arithmetic in Chapter 3.

Chapter 4 is devoted to the description and use of CADNA (Control of Accuracy and Debugging of Numerical Algorithms). This software implements the CESTAC method and discrete stochastic arithmetic.

Chapters 5 and 6 are devoted to the contribution of CADNA software to various numerical calculation methods (direct, iterative and approximate), and to examples of its use. Chapter 7 concludes.

All the introductions to these questions can be found in the [AF 1 470] folder, while the documentation is available at [Doc. AF 1 470] .