A Study of Periodic Motions in Homogeneous Nonlinear Multivariable Systems Written in the Polynomial Vector-Matrix Representation

2020 ◽  
Vol 59 (1) ◽  
pp. 1-7
Author(s):  
B. G. Il’yasov ◽  
G. A. Saitova
Keyword(s):  
Matrix Representation ◽  
Multivariable Systems ◽  
Polynomial Vector ◽  
Periodic Motions ◽  
Vector Matrix

An expanded matrix representation for multivariable systems

1964 ◽  
Vol 9 (4) ◽  
pp. 588-589
Author(s):  
W. Vetter ◽  
W. Miller ◽  
L. McBride
Keyword(s):  
Matrix Representation ◽  
Multivariable Systems

scholarly journals A Parallel Algorithm for Dividing Octonions

Algorithms ◽  
2021 ◽  
Vol 14 (11) ◽  
pp. 309
Author(s):  
Aleksandr Cariow ◽  
Janusz P. Paplinski
Keyword(s):  
Parallel Algorithm ◽  
Matrix Representation ◽  
Specific Structure ◽  
Matrix Product ◽  
Naive Method ◽  
The Matrix ◽  
Speed Up ◽  
Vector Matrix

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.

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