|
This article is cited in 4 scientific papers (total in 4 papers)
NUMERICAL METHODS AND DATA ANALYSIS
Number systems in modular rings and their applications to "error-free" computations
V. M. Chernovab a Samara National Research University, Moskovskoye shosse 34, 443086, Samara, Russia
b IPSI RAS – Branch of the FSRC “Crystallography and Photonics” RAS,
Molodogvardeyskaya 151, 443001, Samara, Russia
Abstract:
The article introduces and explores new systems of parallel machine arithmetic associated with the representation of data in the redundant number system with the basis, the formative sequences of degrees of roots of the characteristic polynomial of the second order recurrence. Such number systems are modular reductions of generalizations of Bergman's number system with the base equal to the "Golden ratio". The associated Residue Number Systems is described. In particular, a new "error-free" algorithm for calculating discrete cyclic convolution is proposed as an application to the problems of digital signal processing. The algorithm is based on the application of a new class of discrete orthogonal transformations, for which there are effective “multipication-free” implementations.
Keywords:
number system, modular arithmetic, discrete convolution, residue number systems.
Received: 31.07.2019 Accepted: 05.09.2019
Citation:
V. M. Chernov, “Number systems in modular rings and their applications to "error-free" computations”, Computer Optics, 43:5 (2019), 901–911
Linking options:
https://www.mathnet.ru/eng/co715 https://www.mathnet.ru/eng/co/v43/i5/p901
|
Statistics & downloads: |
Abstract page: | 214 | Full-text PDF : | 56 | References: | 13 |
|