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Optimization Algorithm for Reduction the Size of Dixon Resultant Matrix: A Case Study on Mechanical Application

Shang Zhang1, *, Seyedmehdi Karimi2, Shahaboddin Shamshirband3, 4, *, Amir Mosavi5,6
1 College of Computer and Information Technology, China Three Gorges University, Yichang, China.
2 Department of Mathematics, Jouybar branch, Islamic Azad University, Jouybar, Iran.
3 Department for Management of Science and Technology Development, Ton Duc Thang University, Ho Chi Minh City, Vietnam.
4 Faculty of Information Technology, Ton Duc Thang University, Ho Chi Minh City, Vietnam.
5 Department Institute of Structural Mechanics, Bauhaus University of Weimar, Germany.
6 Institute of Automation, Kando Kalman Faculty of Electrical Engineering, Obuda University, 1431 Budapest, Hungary.
* Corresponding Authors: Shang Zhang. Email: ;
  Shahaboddin Shamshirband. Email: .

Computers, Materials & Continua 2019, 58(2), 567-583. https://doi.org/10.32604/cmc.2019.02795

Abstract

In the process of eliminating variables in a symbolic polynomial system, the extraneous factors are referred to the unwanted parameters of resulting polynomial. This paper aims at reducing the number of these factors via optimizing the size of Dixon matrix. An optimal configuration of Dixon matrix would lead to the enhancement of the process of computing the resultant which uses for solving polynomial systems. To do so, an optimization algorithm along with a number of new polynomials is introduced to replace the polynomials and implement a complexity analysis. Moreover, the monomial multipliers are optimally positioned to multiply each of the polynomials. Furthermore, through practical implementation and considering standard and mechanical examples the efficiency of the method is evaluated.

Keywords

Dixon resultant matrix, symbolic polynomial system, elimination theory, optimization algorithm, computational complexity.

Cite This Article

S. Zhang, S. Karimi, S. Shamshirband and A. Mosavi, "Optimization algorithm for reduction the size of dixon resultant matrix: a case study on mechanical application," Computers, Materials & Continua, vol. 58, no.2, pp. 567–583, 2019.

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This work is licensed under a Creative Commons Attribution 4.0 International License , which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
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