On isolation of singular zeros of multivariate analytic systems

Kisun Lee; Nan Li; Lihong Zhi

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arXiv · 1904.07937

On isolation of singular zeros of multivariate analytic systems

Kisun Lee·Nan Li·Lihong Zhi

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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 $D^2f(x)$ 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.

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Kisun Lee, Nan Li, Lihong Zhi. 2023-05-18. On isolation of singular zeros of multivariate analytic systems. https://arxiv.org/abs/1904.07937

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