COMPUTATION OF SIMPLE AND GROUP FACTORS OF MULTIVARIATE POLYNOMIALS

This paper generalizes a recent result on simple factorization of 2-va riable (2-v) polynomials to simple and group factorization of n-variat e (n-v), (n greater than or equal to 3) polynomials. The emphasis is o n developing a reliable numerical technique for factorization, It is s hown that simple as well as group factorization can be achieved by per forming singular value decomposition (SVD) on certain matrices obtaine d from the coefficients of the given n-v polynomial expressed in a Kro necker product form. For the polynomials that do not have ''exact'' si mple and/or group factors, the concepts of approximate simple and grou p factorization are developed. The use of SVD leads to an elegant solu tion of an approximate factorization problem. Several nontrivial examp les are included to illustrate the results presented in this paper.