Reliable Implementation of Real Number Algorithms: Theory and Practice

A large amount of the capacity of today's computers is used for computations that can be described as computations involving real numbers. In this book, the focus is on a problem arising particularly in real number computations: the problem of veri?edor reliablecomputations. Since real numbersare objects c- taining an in?nite amount of information, they cannot be represented precisely on a computer. This leads to the well-known problems caused by unveri?ed - plementations of real number algorithms using ?nite precision. While this is t- ditionally seen to be a problem in numerical mathematics, there are also several scienti?c communities in computer science that are dealing with this problem. This book is a follow-up of the Dagstuhl Seminar 06021 on Reliable Imp- mentation of Real Number Algorithms: Theory and Practice, which took place January 813, 2006. It was intended to stimulate an exchange of ideas between the di?erent communities that deal with the problem of reliable implementation of real number algorithms either from a theoretical or from a practical point of view. Forty-eight researchers from many di?erent countries and many di?erent disciplines gathered in the castle of Dagstuhl to exchange views and ideas, in a relaxed atmosphere. The program consisted of 35 talks of 30 minutes each, and of three evening sessions with additional presentations and discussions. There were also lively discussions about di?erent theoretical models and practical - proaches for reliable real number computations.

Klappentext

This book constitutes the revised papers of the International Seminar on Reliable Implementation of Real Number Algorithms, held at Dagstuhl Castle, Germany, in January 2006.

The Seminar was inteded to stimulate an exchange of ideas between the different communities that deal with the problem of reliable implementation of real number algorithms. Topics included formal proofs, software libraries, systems and platforms, as well as computational geometry and solid modelling.

Inhalt
Validated Modeling of Mechanical Systems with SmartMOBILE: Improvement of Performance by ValEncIA-IVP.- Interval Subroutine Library Mission.- Convex Polyhedral Enclosures of Interval-Based Hierarchical Object Representations.- Real Algebraic Numbers: Complexity Analysis and Experimentation.- Verified Methods in Stochastic Traffic Modelling.- Interval Arithmetic Using SSE-2.- Worst Cases for the Exponential Function in the IEEE 754r decimal64 Format.- Robustness and Randomness.- Topological Neighborhoods for Spline Curves: Practice & Theory.- Homotopy Conditions for Tolerant Geometric Queries.- Transfinite Interpolation for Well-Definition in Error Analysis in Solid Modelling.- Theory of Real Computation According to EGC.