Numerical Software with Result Verification

After a short presentation of the paradigms of object oriented programming and interval arithmetic the languages C++ and Java are treated in more detail. Language features are regarded with respect to their support for the definition or application of interval arithmetic. In the final section the 4 libraries Profil/BIAS, C-XSC, filib++ as well as Sun Forte C++ are compared with respect to functionality and efficiency.

[1]  Luc Jaulin,et al.  Nonlinear bounded-error state estimation of continuous-time systems , 2002, Autom..

[2]  Pascal Van Hentenryck,et al.  A Constraint Satisfaction Approach to a Circuit Design Problem , 1996, J. Glob. Optim..

[3]  Pascal Van Hentenryck,et al.  Numerica: A Modeling Language for Global Optimization , 1997, IJCAI.

[4]  David A. McAllester,et al.  Solving Polynomial Systems Using a Branch and Prune Approach , 1997 .

[5]  Arie E. Kaufman,et al.  Parallel Spatial Enumeration of Implicit Surfaces Using Interval Arithmetic for Octree Generation an , 1998 .

[6]  Eric Walter,et al.  Guaranteed Nonlinear State Estimator for Cooperative Systems , 2004, Numerical Algorithms.

[7]  Eric Walter,et al.  Guaranteed nonlinear parameter estimation from bounded-error data via interval analysis , 1993 .

[8]  S. Vavasis.  Nonlinear optimization: complexity issues , 1991 .

[9]  Daniel Richardson,et al.  The Uniformity Conjecture , 2000, CCA.

[10]  Eric Walter,et al.  Guaranteed recursive non‐linear state bounding using interval analysis , 2002 .

[11]  Martin Berz,et al.  Verified Integration of ODEs and Flows Using Differential Algebraic Methods on High-Order Taylor Models , 1998, Reliab. Comput..

[12]  S. G. Rabinovich.  Measurement Errors: Theory and Practice , 1994 .

[13]  Yahia Lebbah,et al.  A Global Filtering Algorithm for Handling Systems of Quadratic Equations and Inequations , 2002, CP.

[14]  E. Walter,et al.  Exact recursive polyhedral description of the feasible parameter set for bounded-error models , 1989 .

[15]  Eldon Hansen,et al.  Global optimization using interval analysis , 1992, Pure and applied mathematics.

[16]  Barry O'Sullivan,et al.  Constraint-Aided Conceptual Design , 2002, Engineering research series.

[17]  Hal L. Smith,et al.  Monotone Dynamical Systems: An Introduction To The Theory Of Competitive And Cooperative Systems (Mathematical Surveys And Monographs) By Hal L. Smith , 1995 .

[18]  Y. F. Huang,et al.  On the value of information in system identification - Bounded noise case , 1982, Autom..

[19]  N. Nedialkov,et al.  Computing rigorous bounds on the solution of an initial value problem for an ordinary differential equation , 1999 .

[20]  Eric Walter,et al.  Guaranteed non-linear estimation using constraint propagation on sets , 2001 .

[21]  Philippe Nivlet,et al.  Propagating Interval Uncertainties In Supervised Pattern Recognition For Reservoir Characterization , 2001 .

[22]  Eric Walter,et al.  Set inversion via interval analysis for nonlinear bounded-error estimation , 1993, Autom..

[23]  Arnaud Gotlieb,et al.  Dynamic Optimization of Interval Narrowing Algorithms , 1998, J. Log. Program..

[24]  F. Chernousko.  State Estimation for Dynamic Systems , 1993 .

[25]  Ralph R. Martin,et al.  Interval and Affine Arithmetic for Surface Location of Power- and Bernstein-Form Polynomials , 2000, IMA Conference on the Mathematics of Surfaces.

[26]  J. Gouzé,et al.  Interval observers for uncertain biological systems , 2000 .

[27]  Eric Walter,et al.  Guaranteed Set Computation with Subpavings , 2001 .

[28]  N. Rowe.  Absolute Bounds on the Mean and Standard Deviation of Transformed Data for Constant-Sign-Derivative Transformations , 1988 .

[29]  Fred C. Schweppe,et al.  Uncertain dynamic systems , 1973 .

[30]  A. Kurzhanski,et al.  Ellipsoidal Calculus for Estimation and Control , 1996 .

[31]  André Vellino,et al.  Constraint Arithmetic on Real Intervals , 1993, WCLP.

[32]  Philippe Nivlet,et al.  A new methodology to account for uncertainties in 4D seismic interpretation , 2001 .

[33]  Boi Faltings,et al.  Consistency techniques for continuous constraints , 1996, Constraints.

[34]  T. Başar,et al.  A New Approach to Linear Filtering and Prediction Problems , 2001 .

[35]  Fabrice Rouillier,et al.  Motivations for an Arbitrary Precision Interval Arithmetic and the MPFI Library , 2005, Reliab. Comput..

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

[37]  Olivier Lhomme,et al.  Consistency Techniques for Numeric CSPs , 1993, IJCAI.

[38]  Stefan Ratschan,et al.  Continuous First-Order Constraint Satisfaction , 2002, AISC.

[39]  Arthur Gelb,et al.  Applied Optimal Estimation , 1974 .

[40]  Kiyotaka Yamamura.  Interval Analysis Using Linear Programming , 1997 .

[41]  Luc Jaulin,et al.  Applied Interval Analysis , 2001, Springer London.

[42]  M. Berz,et al.  Efficient high-order methods for ODEs and DAEs , 2000 .

[43]  P. Walley.  Statistical Reasoning with Imprecise Probabilities , 1990 .

[44]  Klaus Weihrauch,et al.  Computable Analysis , 2005, CiE.

[45]  Michel Kieffer,et al.  Estimation ensembliste par analyse par intervalles Application à la localisation d'un véhicule , 1999 .

[46]  Martin Berz,et al.  Verified High-Order Integration of DAEs and Higher-Order ODEs , 2001 .