Certified numerical real root isolation for bivariate nonlinear systems. (January 2023)

• Record Type: Journal Article
• Authors: Cheng, Jin-San; Wen, Junyi; Zhang, Bingwei
• Is Part Of: Journal of symbolic computation. Volume 114(2023)
• Page Start: 149
• Page End: 171
• Publication Date: 2023-01
• Subjects: Real root isolation -- Opposite monotone system -- Bivariate analytic function -- Uniqueness and existence; Mathematics -- Data processing -- Periodicals; Numerical analysis -- Data processing -- Periodicals; Automatic programming (Computer science) -- Periodicals; Mathématiques -- Informatique -- Périodiques; Analyse numérique -- Informatique -- Périodiques; Programmation automatique -- Périodiques; Automatic programming (Computer science); Mathematics -- Data processing; Numerical analysis -- Data processing; Periodicals; Electronic journals; 510.285
• DOI: 10.1016/j.jsc.2022.04.005
• Languages: English
• ISSNs: 0747-7171

Abstract

Abstract: In this paper, we present a new method for isolating real roots of a bivariate nonlinear system. It is a subdivision method based on analyzing the local geometrical properties of the given system. We propose the concept of opposite monotone system in a box and use it to determine the existence and the uniqueness of a simple real zero of the system in the box. We have implemented our method and the experiments show the effectivity and efficiency of our approach, especially for high degree sparse polynomial systems. This paper is an extended version of the ISSAC'19 conference paper (Cheng and Wen (2019) ).