**PRecision
Estimation
and
Control In
Scientific
and
Engineering
computing**

**Software produced in the framework
of the European**
**Project PINEAPL coordinated
by NAG Ltd.**
**(4th Framework Programme #20018)**

PRECISE is a set of tools provided to help the user
set up computer experiments
to explore the impact of finite precision on the quality of convergence of numerical methods. Because stability is at the heart of the phenomenon under study -- mathematical as well as numerical stabilities --, PRECISE allows users to investigate stability by a straightforward randomization of selected data, then let the computer produce a sample of perturbed solutions and associated residuals, or a sample of perturbed spectra. It allows users to perform a complete statistical backward error analysis on a numerical method or an algorithm to solve a general nonlinear problem of the form $F(x) = y$ (matrix or polynomial equation), at regular points, and in the neighborhood of algebraic singularities. It provides an estimate of the distance to the nearest singularity viewed by the computer, as well as of the order of this singularity. In the case of matrix computations, it can also help to investigate robustness to spectral instability by means of graphical display of perturbed spectra.
F.
Chaitin-Chatelin and V. Fraysse, Lectures on Finite Precision Computations,
1996, SIAM. |