On types of degenerate critical points of real polynomial functions. (July 2020)

• Record Type: Journal Article
• Authors: Guo, Feng; Phạm, Tiến-Sơn
• Is Part Of: Journal of symbolic computation. Volume 99(2020)
• Page Start: 108
• Page End: 126
• Publication Date: 2020-07
• Subjects: 65K05 -- 68W30; Polynomial functions -- Critical points -- Degenerate -- Types -- Tangency varieties; 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.2019.03.004
• Languages: English
• ISSNs: 0747-7171

Abstract

Abstract: In this paper, we consider the problem of identifying the type (local minimizer, maximizer or saddle point) of a given isolated real critical point c, which is degenerate, of a multivariate polynomial function f . To this end, we introduce the definition of faithful radius of c by means of the curve of tangency of f . We show that the type of c can be determined by the global extrema of f over the Euclidean ball centered at c with a faithful radius. We propose algorithms to compute faithful radius of c and determine its type.