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Abstract: 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 parallelization of computations. The computation of two Dirac numbers product using the naïve method takes 256 real multiplications and 240 real additions, while the proposed algorithm… (More)

- Alexandr Cariow, Galina Cariowa
- 2014

In this paper we introduce efficient algorithm for the multiplication of trigintaduonions. The direct multiplication of two trigintaduonions requires 1024 real multiplications and 992 real additions. We show how to compute a trigintaduonion product with 498 real multiplications and 943 real additions. During synthesis of the discussed algorithm we use a… (More)

- Aleksandr Cariow, Galina Cariowa, Jaroslaw Knapinski
- ArXiv
- 2015

Abstract. We present an efficient algorithm to multiply two hyperbolic (countercomplex) octonions. The direct multiplication of two hyperbolic octonions requires 64 real multiplications and 56 real additions. More effective solutions still do not exist. We show how to compute a product of the hyperbolic octonions with 26 real multiplications and 92 real… (More)

- Aleksandr Cariow, Galina Cariowa
- Inf. Process. Lett.
- 2013

- Aleksandr Cariow, Galina Cariowa
- ArXiv
- 2015

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 implementation. The computation of two Dirac numbers product using the naïve method takes 256 real multiplications and 240 real additions, while the proposed algorithm can compute the same… (More)

- Aleksandr Cariow, Galina Cariowa, Bartosz Kubsik
- ArXiv
- 2015

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 real additions. More effective solutions still do not exist. We show how to compute a product of the split-octonions with 28 real multiplications and 92 real additions. During… (More)

- Aleksandr Cariow, Galina Cariowa
- Central European Journal of Computer Science
- 2012

In this paper we introduce efficient algorithm for the multiplication of sedenions. The direct multiplication of two sedenions requires 256 real multiplications and 240 real additions. We show how to compute a sedenions product with 120 real multiplications and 344 real additions.

- Aleksandr Cariow, Galina Cariowa, Rafal Lentek
- ArXiv
- 2015

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 additions. The proposed algorithm can compute the same result with only 512 real multiplications and 576 real additions. The derivation of our algorithm is based on utilizing the fact… (More)

- Aleksandr Cariow, Galina Cariowa
- ArXiv
- 2017

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 some number of general-purpose binary multipliers. The advantage of our solutions is a removing of multiplications through replacing them by less costly squarers. We use Logan's… (More)

- Aleksandr Cariow, Galina Cariowa
- ArXiv
- 2016

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 complete elimination of multiplications and replacing them by less costly squarings. Our approach uses Logan's identity, which proposes to replace the calculation of the product of… (More)