Kybernetika

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.