Abstract:

In this paper, an extension of an $m$-D (multidimensional or multivariable) polynomial factorization method is investigated. The method is the "root perturbation method'' which is recently proposed by the author. According to this method, one sets to zero all complex variables, except one variable, and factorizes the 1-D polynomial. Furthermore, the values of these variables vary properly. In this way, one can "built'' the $m$-dimensional polynomial in its factorized form. However, in the "root perturbation method'', an assumption is that the 1-D polynomial must have discrete roots. In this paper, a solution is given in the case that the 1-D polynomial may have multiple roots. This is achieved by a proper transformation of the complex variables. The present method is summarized by way of algorithm. A numerical (3-D) example is presented.