An Algorithm for Optimizing the Size of Dixon Resultant Matrix

  • Seyedmehdi Karimi Department of Mathematics, Jouybar branch, Islamic Azad University, Jouybar, IRAN
  • Shahab Shamshirband Faculty of Information Technology, Ton Duc Thang University, Ho Chi Minh City, Vietnam
  • Amir Mosavi Department Institute of Structural Mechanics, Bauhaus University of Weimar, GERMANY
  • Shang Zhang College of Computer and Information Technology, China Three Gorges University, Yichang, China.
Keywords: polynomial system, Elimination theory, Dixon resultant matrix, Optimization algorithm, Computational complexity


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 in the polynomial system. Moreover, the monomial multipliers are optimally positioned to multiply each of the polynomials. Further, the optimization algorithm has been used in terms of complexity analysis. Implementation of this method on standard examples proves the high efficiency the method.

Author Biography

Shahab Shamshirband, Faculty of Information Technology, Ton Duc Thang University, Ho Chi Minh City, Vietnam

Shahab is an Adjunct Professor at TON DUC THANG University, Vietnam, (2) Adjunct Faculty at Iran Science and Technology University, IRAN, (3) Academic faculty at IAUC, IRAN, (4) Faculty member at University of Malaya, Malaysia and (5) PostDoc research fellow. He received his Ph.D in computer science. from University of Malaya (Kuala Lumpur, Malaysia) and MSc in Artificial Intelligence. He has published more than 200 papers, in refereed international SCI-IF journals (100), international conference proceedings (25), books (10) with more than 3000 citations in Google Scholar (with h-index of 29), and ResearchGate RG Score of 47. He has worked on various funded projects, with grants worth more than 50000 USD. He is on the editorial board of journals and has served as Guest Editor for journals. His major academic interests are in Computational Intelligence,  Data mining in multidiciplinary fields. His articles are ranked in the highly cited papers and most downloaded papers from the top 10 % (2013 till now) in Computer Science according to the WoS.

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