Conference paperKOPŘIVA Jan, KUNOVSKÝ Jiří, ŠÁTEK Václav, KOCINA Filip and TALIC Emir. Numerical integration in the RNS. In: The Proceedings of the 12th Conference Informatics'2013. Košice: Faculty of Electrical Engineering and Informatics, University of Technology Košice, 2013, pp. 318322. ISBN 9788081431272.  Publication language:  english 

Original title:  Numerical integration in the RNS 

Title (cs):  Numerická integrace v RNS 

Pages:  318322 

Proceedings:  The Proceedings of the 12th Conference Informatics'2013 

Conference:  Informatics 2013  12th International Scientific Conference on Informatics 

Place:  Košice, SK 

Year:  2013 

ISBN:  9788081431272 

Publisher:  Faculty of Electrical Engineering and Informatics, University of Technology Košice 

Keywords 

The Residue Number System (RNS), Ordinary Differential Equations (ODEs), Numerical Integration Methods

Annotation 

The Residue Number System (RNS) usually uses integer numbers. The computation is exact from this reason. As some problems like solutions of ordinary differential equations (ODEs) are unsolvable without modification, this paper proposes a transformation from the integer binary RNS to the floating point binary RNS. The computation using the floating point numbers is exact after the transformation. Solutions of ODEs are presented in the paper. Onestep integration methods (Euler, Heun, RungeKutta) are adapted to RNS to solve simple ODEs with exact precision. 
BibTeX: 

@INPROCEEDINGS{
author = {Jan Kop{\v{r}}iva and Ji{\v{r}}{\'{i}} Kunovsk{\'{y}} and
V{\'{a}}clav {\v{S}}{\'{a}}tek and Filip Kocina and Emir
Talic},
title = {Numerical integration in the RNS},
pages = {318322},
booktitle = {The Proceedings of the 12th Conference Informatics'2013},
year = {2013},
location = {Ko{\v{s}}ice, SK},
publisher = {Faculty of Electrical Engineering and Informatics,
University of Technology Ko{\v{s}}ice},
ISBN = {9788081431272},
language = {english},
url = {http://www.fit.vutbr.cz/research/view_pub.php?id=10444}
} 
