Dixon Multiplier Resultant Matrices

ABSTRACT

  New methods for contructing matrices to compute the resultant
of a polynomial system are proposed and investigated. The
construction is shown to be quite simple and to have low
complexity compared with similar methods. It establishes a
link between Dixon and Newton Sparse (multiplier) methods,
as Bezout matrix is related to Sylvester, and therefore new
method is called Dixon multiplier. Previous results only 
applicable to Dixon resultant method or just to multiplier
methods carry over to Dixon multiplier method, hence inheriting
wide applicability of Dixon method, and easy of manipulation
of multiplier methods. The new construction was applied to
number of practical and theoretical interest examples, showing
its advantages over competing methods.