A Parallel Algorithm for Dividing Octonions
The article presents a parallel hardware-oriented algorithm designed to speed up the division of two octonions. The advantage of the proposed algorithm is that the number of real multiplications is halved as compared to the naive method for implementing this operation. In the synthesis of the discus...
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MDPI AG
2021
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oai:doaj.org-article:9eacef866ff6441c989a4f9d84f900022021-11-25T16:13:00ZA Parallel Algorithm for Dividing Octonions10.3390/a141103091999-4893https://doaj.org/article/9eacef866ff6441c989a4f9d84f900022021-10-01T00:00:00Zhttps://www.mdpi.com/1999-4893/14/11/309https://doaj.org/toc/1999-4893The article presents a parallel hardware-oriented algorithm designed to speed up the division of two octonions. The advantage of the proposed algorithm is that the number of real multiplications is halved as compared to the naive method for implementing this operation. In the synthesis of the discussed algorithm, the matrix representation of this operation was used, which allows us to present the division of octonions by means of a vector–matrix product. Taking into account a specific structure of the matrix multiplicand allows for reducing the number of real multiplications necessary for the execution of the octonion division procedure.Aleksandr CariowJanusz P. PaplinskiMDPI AGarticlehypercomplex numbersdivision of octonionsfast algorithmIndustrial engineering. Management engineeringT55.4-60.8Electronic computers. Computer scienceQA75.5-76.95ENAlgorithms, Vol 14, Iss 309, p 309 (2021) |
| institution |
DOAJ |
| collection |
DOAJ |
| language |
EN |
| topic |
hypercomplex numbers division of octonions fast algorithm Industrial engineering. Management engineering T55.4-60.8 Electronic computers. Computer science QA75.5-76.95 |
| spellingShingle |
hypercomplex numbers division of octonions fast algorithm Industrial engineering. Management engineering T55.4-60.8 Electronic computers. Computer science QA75.5-76.95 Aleksandr Cariow Janusz P. Paplinski A Parallel Algorithm for Dividing Octonions |
| description |
The article presents a parallel hardware-oriented algorithm designed to speed up the division of two octonions. The advantage of the proposed algorithm is that the number of real multiplications is halved as compared to the naive method for implementing this operation. In the synthesis of the discussed algorithm, the matrix representation of this operation was used, which allows us to present the division of octonions by means of a vector–matrix product. Taking into account a specific structure of the matrix multiplicand allows for reducing the number of real multiplications necessary for the execution of the octonion division procedure. |
| format |
article |
| author |
Aleksandr Cariow Janusz P. Paplinski |
| author_facet |
Aleksandr Cariow Janusz P. Paplinski |
| author_sort |
Aleksandr Cariow |
| title |
A Parallel Algorithm for Dividing Octonions |
| title_short |
A Parallel Algorithm for Dividing Octonions |
| title_full |
A Parallel Algorithm for Dividing Octonions |
| title_fullStr |
A Parallel Algorithm for Dividing Octonions |
| title_full_unstemmed |
A Parallel Algorithm for Dividing Octonions |
| title_sort |
parallel algorithm for dividing octonions |
| publisher |
MDPI AG |
| publishDate |
2021 |
| url |
https://doaj.org/article/9eacef866ff6441c989a4f9d84f90002 |
| work_keys_str_mv |
AT aleksandrcariow aparallelalgorithmfordividingoctonions AT januszppaplinski aparallelalgorithmfordividingoctonions AT aleksandrcariow parallelalgorithmfordividingoctonions AT januszppaplinski parallelalgorithmfordividingoctonions |
| _version_ |
1718413272171937792 |