An Answer to an Open Problem on the Multivariate Bernstein Polynomials on a Simplex

被引:1
|
作者
Gavrea, Ioan [1 ]
Ivan, Mircea [1 ]
机构
[1] Tech Univ Cluj Napoca, Str Memorandumului 28, Cluj Napoca 400114, Romania
关键词
Multivariate Bernstein polynomials; simplex; convexity; CONJECTURE;
D O I
10.1007/s00025-018-0938-y
中图分类号
O29 [应用数学];
学科分类号
070104 ;
摘要
We answer and generalize an open problem on the two-dimensional Bernstein polynomials on the unit triangle.
引用
收藏
页数:4
相关论文
共 50 条
  • [21] Convex analysis in the semiparametric model with Bernstein polynomials
    Jianhua Ding
    Zhongzhan Zhang
    Journal of the Korean Statistical Society, 2015, 44 : 58 - 67
  • [22] Simple formula for integration of polynomials on a simplex
    Lasserre, Jean B.
    BIT NUMERICAL MATHEMATICS, 2021, 61 (02) : 523 - 533
  • [23] Simple formula for integration of polynomials on a simplex
    Jean B. Lasserre
    BIT Numerical Mathematics, 2021, 61 : 523 - 533
  • [24] Multivariate Stancu operators defined on a simplex
    Yang, RY
    Xiong, JY
    Cao, FL
    APPLIED MATHEMATICS AND COMPUTATION, 2003, 138 (2-3) : 189 - 198
  • [25] On the log-convexity of a Bernstein-like polynomials sequence
    Girjoaba, Adrian
    DOLOMITES RESEARCH NOTES ON APPROXIMATION, 2024, 17 : 59 - 63
  • [26] SHAPE CRITERIA OF BERNSTEIN-BEZIER POLYNOMIALS OVER SIMPLEXES
    HE, TX
    COMPUTERS & MATHEMATICS WITH APPLICATIONS, 1995, 30 (3-6) : 317 - 333
  • [27] Subharmonicity and convexity properties of Bernstein polynomials and Bezier nets on triangles
    Lorente-Pardo, J
    Sablonnière, P
    Serrano-Pérez, MC
    COMPUTER AIDED GEOMETRIC DESIGN, 1999, 16 (04) : 287 - 300
  • [28] Shape-constrained estimation in functional regression with Bernstein polynomials
    Ghosal, Rahul
    Ghosh, Sujit
    Urbanek, Jacek
    Schrack, Jennifer A.
    Zipunnikov, Vadim
    COMPUTATIONAL STATISTICS & DATA ANALYSIS, 2023, 178
  • [29] Bernstein polynomial angular densities of multivariate extreme value distributions
    Hanson, Timothy E.
    de Carvalho, Miguel
    Chen, Yuhui
    STATISTICS & PROBABILITY LETTERS, 2017, 128 : 60 - 66
  • [30] Multivariate approximation by a combination of modified Taylor polynomials
    Guessab, Allal
    Nouisser, Otheman
    Schmeisser, Gerhard
    JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS, 2006, 196 (01) : 162 - 179