Fast fraction-free triangularization of Bézoutians with applications to sub-resultant chain computation
It is shown that a variant of Gaussian elimination can be applied to factor a permuted Bézoutian and keep the structural properties of the Schur complements unchanged. This process provides a fast division-free algorithm for computing a polynomial remainder sequence of two polynomials. It is pointed out that the same result holds for polynomials having coefficients over a general integral domain. A strategy, that leads to a method for computing the \(LDL^T\) factorization of a permuted Bézoutian that is useful in the solution of root localization problems, is presented.
scientific article; zbMATH DE number 1371008
scientific article