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 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.

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