2011/02/23 by Jin-San Cheng, Xiao-Shan Gao, Cheng, Jin-San +3
Computer Science · Engineering · Mathematics · #Advanced Numerical Analysis Techniques #Algebraic Geometry and Number Theory #FOS: Computer and information sciences #Polynomial and algebraic computation #Symbolic Computation (cs.SC) #cs.SC
paper · pdf · doi:10.48550/arxiv.1102.4681
19 pages,2 figures; MM-Preprint of KLMM, Vol. 29, 92-111, Aug. 2010
arxiv created 2011/02/23 · openalex publication_date 2011/02/23 · arxiv updated 2011/02/24 · openalex created_date 2019/06/27 · openalex updated_date 2026/07/28
In this paper, a linear univariate representation for the roots of a zero-dimensional polynomial equation system is presented, where the roots of the equation system are represented as linear combinations of roots of several univariate polynomial equations. The main advantage of this representation is that the precision of the roots can be easily controlled. In fact, based on the linear univariate representation, we can give the exact precisions needed for roots of the univariate equations in order to obtain the roots of the equation system to a given precision. As a consequence, a root isolation algorithm for a zero-dimensional polynomial equation system can be easily derived from its linear univariate representation.