The application of modular arithmetic for matrix calculations

Abstract

The article considers the application of the Residue Number System (RNS) for matrix calculations. This can be useful to improve the performance and reliability of calculations in digital signal processing and artificial neural networks. We have reviewed the algorithms for calculating the scalar product. Their modeling and comparison with the standard means of the NumPy library of the Python are carried out. Methods of translation between the positional numeral system and RNS are described and simulated. Conclusions about the applicability of methods for calculations on Python are made. We have present the fault-tolerant scheme for error detection and correction. The examples of error occurrence and their correction by the presented scheme are considered