11 citations · 23 across the 11 of their papers we have counts for
11 papers
An algorithm for dividing quaternions
Aleksandr Cariow, Galina Cariowa
In this work, a rationalized algorithm for calculating the quotient of two quaternions is presented which reduces the number of underlying real multiplications. Hardware for fast m…
Minimal Filtering Algorithms for Convolutional Neural Networks
Aleksandr Cariow, Galina Cariowa
In this paper, we present several resource-efficient algorithmic solutions regarding the fully parallel hardware implementation of the basic filtering operation performed in the co…
Hardware-Efficient Structure of the Accelerating Module for Implementation of Convolutional Neural Network Basic Operation
Aleksandr Cariow, Galina Cariowa
This paper presents a structural design of the hardware-efficient module for implementation of convolution neural network (CNN) basic operation with reduced implementation complexi…
Some Schemes for Implementation of Arithmetic Operations with Complex Numbers Using Squaring Units
Aleksandr Cariow, Galina Cariowa
In this paper, new schemes for a squarer, multiplier and divider of complex numbers are proposed. Traditional structural solutions for each of these operations require the presence…
Hardware-Efficient Schemes of Quaternion Multiplying Units for 2D Discrete Quaternion Fourier Transform Processors
Aleksandr Cariow, Galina Cariowa, Marina Chicheva
In this paper, we offer and discuss three efficient structural solutions for the hardware-oriented implementation of discrete quaternion Fourier transform basic operations with red…
A Hardware-Efficient Approach to Computing the Rotation Matrix from a Quaternion
Aleksandr Cariow, Galina Cariowa
In this paper, we have proposed a novel VLSI-oriented approach to computing the rotation matrix entries from the quaternion coefficients. The advantage of this approach is the comp…
An algorithm for multipication of Kaluza numbers
Aleksandr Cariow, Galina Cariowa, Rafał Łentek
This paper presents the derivation of a new algorithm for multiplying of two Kaluza numbers. Performing this operation directly requires 1024 real multiplications and 992 real addi…
An algorithm for multiplication of split-octonions
Aleksandr Cariow, Galina Cariowa, Bartosz Kubsik
In this paper we introduce efficient algorithm for the multiplication of split-octonions. The direct multiplication of two split-octonions requires 64 real multiplications and 56 r…
Derivation of a low multiplicative complexity algorithm for multiplying hyperbolic octonions
Aleksandr Cariow, Galina Cariowa, Jaroslaw Knapinski
We present an efficient algorithm to multiply two hyperbolic octonions. The direct multiplication of two hyperbolic octonions requires 64 real multiplications and 56 real additions…
A new algorithm for multiplying two Dirac numbers
Aleksandr Cariow, Galina Cariowa
In this work a rationalized algorithm for Dirac numbers multiplication is presented. This algorithm has a low computational complexity feature and is well suited to FPGA implementa…
A Hardware-oriented Algorithm for Complex-valued Constant Matrix-vector Multiplication
Aleksandr Cariow, Galina Cariowa
In this paper we present a hardware-oriented algorithm for constant matrix-vector product calculating, when the all elements of vector and matrix are complex numbers. The proposed…