The subresultant and clusters of close roots

Authors:
Tateaki Sasaki
Affiliations:
University of Tsukuba, Ibaraki, Japan
Venue:
ISSAC '03 Proceedings of the 2003 international symposium on Symbolic and algebraic computation
Year:
2003

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Abstract

This paper investigates the subresultant of univariate polynomials from the viewpoint of close roots. First, we derive formulas which express the subresultant and its cofactors in the root-differences. Then, we consider the case that the given polynomials contain one or more clusters of mutually close roots of closeness ß. We derive formulas showing the dependences of the coefficients of subresultant and its cofactors on ß and the number of clusters. Finally, we determine the magnitudes of cancellations which occur when we apply the Euclidean algorithm to polynomials having close roots.