A hybrid approach for normal factorization of polynomials

Abstract

The problem considered here is an integral part of computations for algebraic control problems. The paper introduces the notion of normal factorization of polynomials and then presents a new hybrid algorithm for the computation of this factorization. The advantage of such a factorization is that it handles the determination of multiplicities and produces factors of lower degree and with distinct roots. The presented algorithm has the ability to specify the roots of the polynomials without computing them explicitly. Also it may be used for investigating the clustering of the roots of the polynomials. The developed procedure is based on the use of algorithms determining the greatest common divisor of polynomials. The algorithm can be implemented symbolically for the specification of well separated roots and numerically for the specification of roots belonging in approximate clusters. © Springer-Verlag Berlin Heidelberg 2006.