scholarly journals Bounds for Bernstein Basis Functions and Meyer–König and Zeller Basis Functions

1998 ◽  
Vol 219 (2) ◽  
pp. 364-376 ◽  
Author(s):  
Zeng Xiaoming
Keyword(s):  
Basis Functions ◽  
Bernstein Basis ◽  
Bernstein Basis Functions

8-node quasi-conforming plane element by using Bernstein basis functions

2018 ◽  
Vol 70 ◽  
pp. 127-140 ◽  
Author(s):  
Changsheng Wang ◽  
Xingtong Lu ◽  
Xiangkui Zhang ◽  
Ping Hu
Keyword(s):  
Basis Functions ◽  
Bernstein Basis ◽  
Plane Element ◽  
Bernstein Basis Functions

scholarly journals Decomposition of mixed pixels in MODIS data using Bernstein basis functions

2019 ◽  
Vol 13 (04) ◽  
pp. 1
Author(s):  
Yi Qin ◽  
Feng Guo ◽  
Yupeng Ren ◽  
Xin Wang ◽  
Juan Gu ◽  
...  
Keyword(s):  
Basis Functions ◽  
Bernstein Basis ◽  
Modis Data ◽  
Mixed Pixels ◽  
Bernstein Basis Functions

scholarly journals On a New Construction of Generalized q-Bernstein Polynomials Based on Shape Parameter λ

Symmetry ◽  
2021 ◽  
Vol 13 (10) ◽  
pp. 1919
Author(s):  
Qing-Bo Cai ◽  
Reşat Aslan
Keyword(s):  
Error Estimation ◽  
Shape Parameter ◽  
Bernstein Polynomials ◽  
Modulus Of Smoothness ◽  
Basis Functions ◽  
Approximation Properties ◽  
Bernstein Basis ◽  
New Class ◽  
New Construction ◽  
Bernstein Basis Functions

This paper deals with several approximation properties for a new class of q-Bernstein polynomials based on new Bernstein basis functions with shape parameter λ on the symmetric interval [−1,1]. Firstly, we computed some moments and central moments. Then, we constructed a Korovkin-type convergence theorem, bounding the error in terms of the ordinary modulus of smoothness, providing estimates for Lipschitz-type functions. Finally, with the aid of Maple software, we present the comparison of the convergence of these newly constructed polynomials to the certain functions with some graphical illustrations and error estimation tables.

Unimodal properties of B-spline and Bernstein-basis functions

1992 ◽  
Vol 24 (12) ◽  
pp. 627-636 ◽  
Author(s):  
P.J. Barry ◽  
J.C. Beatty ◽  
R.N. Goldman
Keyword(s):  
Basis Functions ◽  
Bernstein Basis ◽  
B Spline ◽  
Bernstein Basis Functions

scholarly journals A Generalized Quasi Cubic Trigonometric Bernstein Basis Functions and Its B-Spline Form

Mathematics ◽  
2021 ◽  
Vol 9 (10) ◽  
pp. 1154
Author(s):  
Yunyi Fu ◽  
Yuanpeng Zhu
Keyword(s):  
Sufficient Conditions ◽  
Total Positivity ◽  
Basis Functions ◽  
Shape Functions ◽  
Bernstein Basis ◽  
B Spline ◽  
Special Cases ◽  
Chebyshev Space ◽  
Spline Basis ◽  
Bernstein Basis Functions

In this paper, under the framework of Extended Chebyshev space, four new generalized quasi cubic trigonometric Bernstein basis functions with two shape functions α(t) and β(t) are constructed in a generalized quasi cubic trigonometric space span{1,sin2t,(1−sint)2α(t),(1−cost)2β(t)}, which includes lots of previous work as special cases. Sufficient conditions concerning the two shape functions to guarantee the new construction of Bernstein basis functions are given, and three specific examples of the shape functions and the related applications are shown. The corresponding generalized quasi cubic trigonometric Bézier curves and the corner cutting algorithm are also given. Based on the new constructed generalized quasi cubic trigonometric Bernstein basis functions, a kind of new generalized quasi cubic trigonometric B-spline basis functions with two local shape functions αi(t) and βi(t) is also constructed in detail. Some important properties of the new generalized quasi cubic trigonometric B-spline basis functions are proven, including partition of unity, nonnegativity, linear independence, total positivity and C2 continuity. The shape of the parametric curves generated by the new proposed B-spline basis functions can be adjusted flexibly.

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