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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Elsevier
2021
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oai:scholar.dlu.edu.vn:123456789-4972022-08-02T23:01:20Z On types of degenerate critical points of real polynomial functions Guo, Feng Phạm, Tiến Sơn Polynomial functions Critical points Degenerate Tangency varieties Types 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. 99 108-126 2021-08-23T04:19:06Z 2021-08-23T04:19:06Z 2020 Journal article Bài báo đăng trên tạp chí quốc tế (có ISSN), bao gồm book chapter http://scholar.dlu.edu.vn/handle/123456789/497 10.1016/j.jsc.2019.03.004 en Journal of Symbolic Computation Journal of Symbolic Computation 99 (2020) 0747-7171 Elsevier |
| institution |
Thư viện Trường Đại học Đà Lạt |
| collection |
Thư viện số |
| language |
English |
| topic |
Polynomial functions Critical points Degenerate Tangency varieties Types |
| spellingShingle |
Polynomial functions Critical points Degenerate Tangency varieties Types Guo, Feng Phạm, Tiến Sơn On types of degenerate critical points of real polynomial functions |
| description |
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. |
| format |
Journal article |
| author |
Guo, Feng Phạm, Tiến Sơn |
| author_facet |
Guo, Feng Phạm, Tiến Sơn |
| author_sort |
Guo, Feng |
| title |
On types of degenerate critical points of real polynomial functions |
| title_short |
On types of degenerate critical points of real polynomial functions |
| title_full |
On types of degenerate critical points of real polynomial functions |
| title_fullStr |
On types of degenerate critical points of real polynomial functions |
| title_full_unstemmed |
On types of degenerate critical points of real polynomial functions |
| title_sort |
on types of degenerate critical points of real polynomial functions |
| publisher |
Elsevier |
| publishDate |
2021 |
| url |
http://scholar.dlu.edu.vn/handle/123456789/497 |
| _version_ |
1768305771482710016 |