Optimization algorithm for reduction the size of Dixon Resultant Matrix: A case study on mechanical application

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.