VerifyRealRoots: A Matlab Package for Computing Verified Real Solutions of Polynomials Systems of Equations and Inequalities

Zhengfeng Yang; Hanrui Zhao; Lihong Zhi

doi:10.1007/s11424-023-1406-7

VerifyRealRoots: A Matlab Package for Computing Verified Real Solutions of Polynomials Systems of Equations and Inequalities

Zhengfeng Yang^*
, Hanrui Zhao^*
, Lihong Zhi^*

^*此作品的通讯作者

软件工程学院

East China Normal University
CAS - Academy of Mathematics and System Sciences
University of Chinese Academy of Sciences

科研成果: 期刊稿件 › 文章 › 同行评审

4 引用（Scopus）

摘要

VerifyRealRoots is a Matlab package for computing and verifying real solutions of polynomial systems of equations and inequalities. It calls Bertini or MMCRSolver for finding approximate real solutions and then applies AINLSS to verify the existence of a regular solution of a polynomial system or applies AINLSS2 (AIVISS) to verify the existence of a double solution (a singular solution of an arbitrary multiplicity) of a slightly perturbed polynomial system.

源语言	英语
页（从-至）	866-883
页数	18
期刊	Journal of Systems Science and Complexity
卷	36
期	2
DOI	https://doi.org/10.1007/s11424-023-1406-7
出版状态	已出版 - 4月 2023

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10.1007/s11424-023-1406-7

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abstract = "VerifyRealRoots is a Matlab package for computing and verifying real solutions of polynomial systems of equations and inequalities. It calls Bertini or MMCRSolver for finding approximate real solutions and then applies AINLSS to verify the existence of a regular solution of a polynomial system or applies AINLSS2 (AIVISS) to verify the existence of a double solution (a singular solution of an arbitrary multiplicity) of a slightly perturbed polynomial system.",

keywords = "Error bounds, polynomial system, real solutions, singular solutions, verification",

author = "Zhengfeng Yang and Hanrui Zhao and Lihong Zhi",

note = "Publisher Copyright: {\textcopyright} 2023, The Editorial Office of JSSC \& Springer-Verlag GmbH Germany.",

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T2 - A Matlab Package for Computing Verified Real Solutions of Polynomials Systems of Equations and Inequalities

AU - Yang, Zhengfeng

AU - Zhao, Hanrui

AU - Zhi, Lihong

PY - 2023/4

Y1 - 2023/4

N2 - VerifyRealRoots is a Matlab package for computing and verifying real solutions of polynomial systems of equations and inequalities. It calls Bertini or MMCRSolver for finding approximate real solutions and then applies AINLSS to verify the existence of a regular solution of a polynomial system or applies AINLSS2 (AIVISS) to verify the existence of a double solution (a singular solution of an arbitrary multiplicity) of a slightly perturbed polynomial system.

AB - VerifyRealRoots is a Matlab package for computing and verifying real solutions of polynomial systems of equations and inequalities. It calls Bertini or MMCRSolver for finding approximate real solutions and then applies AINLSS to verify the existence of a regular solution of a polynomial system or applies AINLSS2 (AIVISS) to verify the existence of a double solution (a singular solution of an arbitrary multiplicity) of a slightly perturbed polynomial system.

KW - Error bounds

KW - polynomial system

KW - real solutions

KW - singular solutions

KW - verification

UR - https://www.scopus.com/pages/publications/85148382133

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DO - 10.1007/s11424-023-1406-7

M3 - 文章

AN - SCOPUS:85148382133

SN - 1009-6124

VL - 36

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JO - Journal of Systems Science and Complexity

JF - Journal of Systems Science and Complexity

IS - 2

ER -

VerifyRealRoots: A Matlab Package for Computing Verified Real Solutions of Polynomials Systems of Equations and Inequalities

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