AN EXTENSION OF THE ROOT PERTURBATION M-DIMENSIONAL POLYNOMIAL FACTORIZATION METHOD

In this paper, an extension of an m-D (multidimensional or multivariab le) 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, ex cept 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 th e ''root perturbation method'', an assumption is that the 1-D polynomi al 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 achieve d by a proper transformation of the complex variables. The present met hod is summarized by way of algorithm. A numerical (3-D) example is pr esented.