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 vi...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.展开更多
Dixon resultant is a basic elimination method which has been used widely in the high technology fields of automatic control, robotics, etc. But how to remove extraneous factors in Dixon resultants has been a very diff...Dixon resultant is a basic elimination method which has been used widely in the high technology fields of automatic control, robotics, etc. But how to remove extraneous factors in Dixon resultants has been a very difficult problem. In this paper, we discover some extraneous factors by expressing the Dixon resultant in a linear combination of original polynomial system. Furthermore, it has been proved that the factors mentioned above include three parts which come from Dixon derived polynomials, Dixon matrix and the resulting resultant expression by substituting Dixon derived polynomials respectively.展开更多
文摘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.
基金supported by the National Key Basic Special Funds of China (Grant No. 2004CB318003)the Knowledge Innovation Project of the Chinese Academy of Sciences (Grant No. KJCX2-YW-S02)+2 种基金the National Natural Science Foundation of China (Grant No. 90718041)Shanghai Leading Academic Discipline Project(Grant No. B412)the Doctor Startup Foundation of East China Normal University (Grant No. 790013J4)
文摘Dixon resultant is a basic elimination method which has been used widely in the high technology fields of automatic control, robotics, etc. But how to remove extraneous factors in Dixon resultants has been a very difficult problem. In this paper, we discover some extraneous factors by expressing the Dixon resultant in a linear combination of original polynomial system. Furthermore, it has been proved that the factors mentioned above include three parts which come from Dixon derived polynomials, Dixon matrix and the resulting resultant expression by substituting Dixon derived polynomials respectively.
