A. Edalat, и R. Heckmann. Applied Semantics, стр. 193--267. Berlin, Heidelberg, Springer Berlin Heidelberg, (2002)
Аннотация
We introduce, in Part I, a number representation suitable for exact real number computation, consisting of an exponent and a mantissa, which is an infinite stream of signed digits, based on the interval −1,1. Numerical operations are implemented in terms of linear fractional transformations (LFT's). We derive lower and upper bounds for the number of argument digits that are needed to obtain a desired number of result digits of a computation, which imply that the complexity of LFT application is that of multiplying n-bit integers. In Part II, we present an accessible account of a domain-theoretic approach to computational geometry and solid modelling which provides a data-type for designing robust geometric algorithms, illustrated here by the convex hull algorithm.
%0 Conference Paper
%1 10.1007/3-540-45699-6_5
%A Edalat, Abbas
%A Heckmann, Reinhold
%B Applied Semantics
%C Berlin, Heidelberg
%D 2002
%E Barthe, Gilles
%E Dybjer, Peter
%E Pinto, Luís
%E Saraiva, João
%I Springer Berlin Heidelberg
%K 2002 computational-geometry computer-science
%P 193--267
%T Computing with Real Numbers
%X We introduce, in Part I, a number representation suitable for exact real number computation, consisting of an exponent and a mantissa, which is an infinite stream of signed digits, based on the interval −1,1. Numerical operations are implemented in terms of linear fractional transformations (LFT's). We derive lower and upper bounds for the number of argument digits that are needed to obtain a desired number of result digits of a computation, which imply that the complexity of LFT application is that of multiplying n-bit integers. In Part II, we present an accessible account of a domain-theoretic approach to computational geometry and solid modelling which provides a data-type for designing robust geometric algorithms, illustrated here by the convex hull algorithm.
%@ 978-3-540-45699-5
@inproceedings{10.1007/3-540-45699-6_5,
abstract = {We introduce, in Part I, a number representation suitable for exact real number computation, consisting of an exponent and a mantissa, which is an infinite stream of signed digits, based on the interval [−1,1]. Numerical operations are implemented in terms of linear fractional transformations (LFT's). We derive lower and upper bounds for the number of argument digits that are needed to obtain a desired number of result digits of a computation, which imply that the complexity of LFT application is that of multiplying n-bit integers. In Part II, we present an accessible account of a domain-theoretic approach to computational geometry and solid modelling which provides a data-type for designing robust geometric algorithms, illustrated here by the convex hull algorithm.},
added-at = {2020-02-07T13:48:28.000+0100},
address = {Berlin, Heidelberg},
author = {Edalat, Abbas and Heckmann, Reinhold},
biburl = {https://www.bibsonomy.org/bibtex/2d4c00be2c08e1f9b4e44143083bc7795/analyst},
booktitle = {Applied Semantics},
description = {Computing with Real Numbers | SpringerLink},
editor = {Barthe, Gilles and Dybjer, Peter and Pinto, Lu{\'i}s and Saraiva, Jo{\~a}o},
interhash = {1a9843a9ed6ff52b74803e7e6495e62f},
intrahash = {d4c00be2c08e1f9b4e44143083bc7795},
isbn = {978-3-540-45699-5},
keywords = {2002 computational-geometry computer-science},
pages = {193--267},
publisher = {Springer Berlin Heidelberg},
timestamp = {2020-02-07T13:48:28.000+0100},
title = {Computing with Real Numbers},
year = 2002
}