On types of degenerate critical points of real polynomial functions
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...
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| Autores principales: | , |
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| Formato: | Journal article |
| Lenguaje: | English |
| Publicado: |
Elsevier
2021
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| Materias: | |
| Acceso en línea: | http://scholar.dlu.edu.vn/handle/123456789/497 |
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| Thư viện lưu trữ: | Thư viện Trường Đại học Đà Lạt |
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| Sumario: | 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. |
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