Computation of simple and group factors of multivariate polynomials

This paper generalizes a recent result onsimple factorization of 2-variable (2-v) polynomials to simple andgroup factorization ofn-variate (n-v), (n3) polynomials. The emphasis is on developing a reliablenumerical technique for factorization. It is shown that simple as well as group factorization can be achieved by performing singular value decomposition (SVD) on certain matrices obtained from the coefficients of the givenn-v polynomial expressed in a Kronecker product form. For the polynomials that do not have exact simple and/or group factors, the concepts of approximate simple and group factorization are developed. The use of SVD leads to an elegant solution of an approximaten factorization problem. Several nontrivial examples are included to illustrate the results presented in this paper.Research supported by WRDC grant F33615-88-C-3605, NSF grant ECS-9110636, and NSERC of Canada grant A1345.