Reliable Implementation of Real Number Algorithms: Theory and Practice

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A large amount of the capacity of todaya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 aReliable Imp- mentation of Real Number Algorithms: Theory and Practice, a which took place January 8a13, 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.Table 1. Instruction Set of Pointer Models TypeName Instruction Effect (G is transformed to G) (i) Pointer Assignment w a w [w]G is new ... Each real pointer machine computes a partial function f : G(R)arG(R) (12) For simplicity, we define26 a semi-numerical problem to also be a partial function of the form (12). The objects of computational geometry can be represented by real tagged graphs (see [43]).

 Title : Reliable Implementation of Real Number Algorithms: Theory and Practice Author : Peter Hertling, Christoph M. Hoffmann, Wolfram Luther, Nathalie Revol Publisher : Springer - 2008-08-06