Reliable Implementation of Real Number Algorithms: Theory and Practice: International Seminar Dagstuhl Castle, Germany, January 8-13, 2006, Revised Papers / Edition 1

by Peter Hertling, Christoph M. Hoffmann, Wolfram Luther, Nathalie Revol

Overview

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 verifiedor reliablecomputations. Since real numbersare objects c- taining an inflnite amount of information, they cannot be represented precisely on a computer. This leads to the well-known problems caused by unverified - plementations of real number algorithms usingfinite precision. While this is t- ditionally seen to be a problem in numerical mathematics, there are also several scientific 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 8–13, 2006. It was intended to stimulate an exchange of ideas between the different 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 different countries and many different 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 different theoretical models and practical - proaches for reliable real number computations.

Product Details

ISBN-13:	9783540855200
Publisher:	Springer Berlin Heidelberg
Publication date:	10/07/2008
Series:	Lecture Notes in Computer Science , #5045
Edition description:	2008
Pages:	239
Product dimensions:	6.10(w) x 9.40(h) x 0.60(d)

Table of Contents

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 Shastic 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.