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The Numerical Algorithms 
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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. 

PRECISE offers the following facilities:  2 modules


For
statistical backward error analysis 
a module for sensitivity analysis
It provides
statistical estimation of



  • condition numbers at regular or H\"older-singular

    • points, for the algorithm/method and the problem, 
  • backward errors, 
  • reliability and quality indexes, 
  • distances to singularity, or dangerous borders, 

    • order of H\"older-singularities. 
     
     

    This module is contained in the Module1 directory. 
    graphical displays of



  • perturbed spectra. 

    • Directory Module2/PtbSpec 
  • spectral portraits and pseudospectra. 

    • Directory Module2/SpPort 
  • sets of pseudosolutions. 

    •  

     
     




    This module is contained in the Module2 directory. 

     

    A complete description of PRECISE is given in 

    F. Chaitin-Chatelin and V. Fraysse, Lectures on Finite Precision Computations, 1996, SIAM.