20 citations · 23 across the 6 of their papers we have counts for
6 papers
Two-step Newton's method for deflation-one singular zeros of analytic systems
Kisun Lee, Nan Li, Lihong Zhi
We propose a two-step Newton's method for refining an approximation of a singular zero whose deflation process terminates after one step, also known as a deflation-one singularity.…
The integral closure of a primary ideal is not always primary
Nan Li, Zijia Li, Zhi-Hong Yang +1
In 1936, Krull asked if the integral closure of a primary ideal is still primary. Fifty years later, Huneke partially answered this question by giving a primary polynomial ideal wh…
Computing Simple Multiple Zeros of Polynomial Systems
Zhiwei Hao, Wenrong Jiang, Nan Li +1
Given a polynomial system f associated with a simple multiple zero x of multiplicity μ, we give a computable lower bound on the minimal distance between the simple multiple zero x…
Verified Error Bounds for Isolated Singular Solutions of Polynomial Systems
Nan Li, Lihong Zhi
In this paper, we generalize the algorithm described by Rump and Graillat, as well as our previous work on certifying breadth-one singular solutions of polynomial systems, to compu…
Verified Error Bounds for Isolated Singular Solutions of Polynomial Systems: Case of Breadth One
Nan Li, Lihong Zhi
In this paper we describe how to improve the performance of the symbolic-numeric method in (Li and Zhi,2009, 2011) for computing the multiplicity structure and refining approximate…
Computing Isolated Singular Solutions of Polynomial Systems: Case of Breadth One
Nan Li, Lihong Zhi
We present a symbolic-numeric method to refine an approximate isolated singular solution of a polynomial system $F=\{f_1, ..., f_…