Aquarels: A Problem-Solving Environment for Validating Scientific Software

Numerical validation has become a major concern in many scientific applications. This paper presents the software environment Aquarels which integrates through a window-based interface various tools to tackle numerical validation. Aquarels includes tools to control floating-point arithmetic, perturbation tools, interval arithmetic, multi-precision arithmetic. Several real-life applications illustrate the efficiency of this software.

[1]  Jean-Michel Muller,et al.  Qualité des calculs sur ordinateur , 1997 .

[2]  C. Loan,et al.  Nineteen Dubious Ways to Compute the Exponential of a Matrix , 1978 .

[3]  Jean-Michel Muller,et al.  Elementary Functions: Algorithms and Implementation , 1997 .

[4]  Pierre Alliez,et al.  Removing Degeneracies by Perturbing the Problem or the World , 1997 .

[5]  William M. Waite,et al.  Software manual for the elementary functions , 1980 .

[6]  Kurt Mehlhorn,et al.  Exact geometric computation in LEDA , 1995, SCG '95.

[7]  J.-M. Muller Algorithmes de division pour microprocesseurs : illustration à l'aide du Bug du Pentium , 1995 .

[8]  John F. Canny,et al.  A General Approach to Removing Degeneracies , 1995, SIAM J. Comput..

[9]  Ansi Ieee,et al.  IEEE Standard for Binary Floating Point Arithmetic , 1985 .

[10]  C. Loan The Sensitivity of the Matrix Exponential , 1977 .

[11]  James Hardy Wilkinson,et al.  Rounding errors in algebraic processes , 1964, IFIP Congress.

[12]  Nicholas J. Higham,et al.  INVERSE PROBLEMS NEWSLETTER , 1991 .

[13]  S. Godunov Guaranteed Accuracy in Numerical Linear Algebra , 1993 .

[14]  M. Porte,et al.  Etude statistique des erreurs dans l'arithmetique des ordinateurs; application au controle des resultats d'algorithmes numeriques , 1974 .

[15]  S. Rump Verification methods for dense and sparse systems of equations , 1994 .

[16]  Françoise Chaitin-Chatelin,et al.  Lectures on finite precision computations , 1996, Software, environments, tools.

[17]  Olivier Devillers Computational geometry and discrete computations , 1996, DGCI.

[18]  William J. Cody,et al.  Algorithm 665: Machar: a subroutine to dynamically determined machine parameters , 1988, TOMS.

[19]  James Demmel,et al.  LAPACK Users' Guide, Third Edition , 1999, Software, Environments and Tools.

[20]  Christopher J. Van Wyk,et al.  Efficient exact arithmetic for computational geometry , 1993, SCG '93.

[21]  Arnaud Tisserand,et al.  Toward Correctly Rounded Transcendentals , 1998, IEEE Trans. Computers.

[22]  A. Neumaier Interval methods for systems of equations , 1990 .

[23]  Paul-Louis George,et al.  Génération automatique de maillages : applications aux méthodes d'éléments finis , 1991 .

[24]  Ulrich W. Kulisch,et al.  A New Arithmetic for Scientific Computation , 1983, IMACS World Congress.