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On isolation of simple multiple zeros and clusters of zeros of polynomial systems


Authors: Zhiwei Hao, Wenrong Jiang, Nan Li and Lihong Zhi
Journal: Math. Comp. 89 (2020), 879-909
MSC (2010): Primary 65H10, 74G35, 68W30, 32-04, 32S99
DOI: https://doi.org/10.1090/mcom/3479
Published electronically: October 1, 2019
MathSciNet review: 4044454
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Abstract: Given a well-constrained polynomial system $ f$ associated with a simple multiple zero $ x$ of multiplicity $ \mu $, we give a computable separation bound for isolating $ x$ from the other zeros of $ f$. When $ x$ is only given with a limited accuracy, we give a numerical criterion for isolating a nearby cluster of $ \mu $ zeros of $ f$ (counting multiplicities) in a ball around $ x$.


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Additional Information

Zhiwei Hao
Affiliation: Key Laboratory of Mathematics Mechanization, Academy of Mathematics and Systems Science, Chinese Academy of Sciences, Beijing 100190, China; and University of Chinese Academy of Sciences, Beijing 100049, China
Email: haozhiwei@mmrc.iss.ac.cn

Wenrong Jiang
Affiliation: Key Laboratory of Mathematics Mechanization, Academy of Mathematics and Systems Science, Chinese Academy of Sciences, Beijing 100190, and China; University of Chinese Academy of Sciences, Beijing 100049, China
Email: jiangwr@amss.ac.cn

Nan Li
Affiliation: College of Mathematics and Statistics, Shenzhen University, Shenzhen 518060, China
Email: nan.li@szu.edu.cn

Lihong Zhi
Affiliation: Key Laboratory of Mathematics Mechanization, Academy of Mathematics and Systems Science, Chinese Academy of Sciences, Beijing 100190, China; and University of Chinese Academy of Sciences, Beijing 100049, China
Email: lzhi@mmrc.iss.ac.cn

DOI: https://doi.org/10.1090/mcom/3479
Received by editor(s): August 20, 2018
Received by editor(s) in revised form: February 21, 2019, and May 6, 2019
Published electronically: October 1, 2019
Additional Notes: This work was carried out when the third author was with Tianjin University. This work was supported in part by the National Key Research Project of China 2018YFA0306702 (Zhi) and the National Natural Science Foundation of China 11571350 (Zhi), 11601378 (Li)
The third author is the corresponding author.
Article copyright: © Copyright 2019 American Mathematical Society