On isolation of singular zeros of multivariate analytic systems

2019/04/16 by Kisun Lee, Nan Li, Lee, Kisun +3
Computer Science · Mathematics · #14Q99 #65D18 #Advanced Optimization Algorithms Research #Algebraic Geometry (math.AG) #FOS: Mathematics #Matrix Theory and Algorithms #Numerical Analysis (math.NA) #Polynomial and algebraic computation

paper · pdf · doi:10.48550/arxiv.1904.07937

openalex publication_date 2019/04/16 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We give a separation bound for an isolated multiple root x of a square multivariate analytic system f satisfying that an operator deduced by adding Df(x) and a projection of D²f(x) in a direction of the kernel of Df(x) is invertible. We prove that the deflation process applied on f and this kind of roots terminates after only one iteration. When x is only given approximately, we give a numerical criterion for isolating a cluster of zeros of f near x. We also propose a lower bound of the number of roots in the cluster.

Citations

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