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
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
In recent years,the Dixon resultant matrix has been used widely in the resultant elimination to solve nonlinear polynomial equations and many researchers have studied its efficient algorithms.The recursive algorithm i...In recent years,the Dixon resultant matrix has been used widely in the resultant elimination to solve nonlinear polynomial equations and many researchers have studied its efficient algorithms.The recursive algorithm is a very efficient algorithm,but which deals with the case of three polynomial equations with two variables at most.In this paper,we extend the algorithm to the general case of n+1 polynomial equations in nvariables.The algorithm has been implemented in Maple 9.By testing the random polyno mial equations,the results demonstrate that the efficiency of our program is much better than the previous methods,and it is exciting that the necessary condition for the existence of common intersection points on four general surfaces in which the degree with respect to every variable is not greater than 2 is given out in 48×48 Dixon matrix firstly by our program.展开更多
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.
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partially supported by the China NKBRSF Project(Grant No.2004CB318003)the"Hundreds Talents Plan"of Institute of Computing Technology,Chinese Academy of Sciences(20044040)
文摘In recent years,the Dixon resultant matrix has been used widely in the resultant elimination to solve nonlinear polynomial equations and many researchers have studied its efficient algorithms.The recursive algorithm is a very efficient algorithm,but which deals with the case of three polynomial equations with two variables at most.In this paper,we extend the algorithm to the general case of n+1 polynomial equations in nvariables.The algorithm has been implemented in Maple 9.By testing the random polyno mial equations,the results demonstrate that the efficiency of our program is much better than the previous methods,and it is exciting that the necessary condition for the existence of common intersection points on four general surfaces in which the degree with respect to every variable is not greater than 2 is given out in 48×48 Dixon matrix firstly by our program.
