Matrix factorization and approximate GCDs

Abstract

This chapter describes some methods for approximate GCD computation which are based upon a rank-revealing factorization, of a resultant matrix. Such factorizations are useful for approximate rank determination, and therefore to determine bounds on the degree of an approximate GCD; a set of coefficients is then derived either from the factorization itself, or using other techniques. The results given by factorization-based methods are sometimes significantly improved by a refinement stage.