(p, q)-Bernstein Bases and Operators over Arbitrary Intervals

2021 ◽  
Author(s):  
Asif Khan ◽  
Vinita Sharma ◽  
Khalid Khan
Keyword(s):  
Bernstein Bases

Chebyshev–Bernstein bases

1999 ◽  
Vol 16 (7) ◽  
pp. 649-669 ◽  
Author(s):  
Marie-Laurence Mazure
Keyword(s):  
Bernstein Bases

Integration of Jacobi and Weighted Bernstein Polynomials Using Bases Transformations

2007 ◽  
Vol 7 (3) ◽  
pp. 221-226 ◽  
Author(s):  
Abedallah Rababah
Keyword(s):  
Jacobi Polynomials ◽  
Bernstein Polynomials ◽  
Definite Integral ◽  
De Casteljau Algorithm ◽  
Bernstein Bases

AbstractThis paper presents methods to compute integrals of the Jacobi polynomials by the representation in terms of the Bernstein — B´ezier basis. We do this because the integration of the Bernstein — B´ezier form simply corresponds to applying the de Casteljau algorithm in an easy way. Formulas for the definite integral of the weighted Bernstein polynomials are also presented. Bases transformations are used. In this paper, the methods of integration enable us to gain from the properties of the Jacobi and Bernstein bases.

scholarly journals Relationships between identities for quantum Bernstein bases and formulas for hypergeometric series

Filomat ◽  
2020 ◽  
Vol 34 (8) ◽  
pp. 2485-2494
Author(s):  
Fatma Zünacı ◽  
Ron Goldman ◽  
Plamen Simeonov
Keyword(s):  
Hypergeometric Series ◽  
Partition Of Unity ◽  
Bernstein Bases ◽  
Marsden Identity

Two seemingly disparate mathematical entities - quantum Bernstein bases and hypergeometric series - are revealed to be intimately related. The partition of unity property for quantum Bernstein bases is shown to be equivalent to the Chu-Vandermonde formula for hypergeometric series, and the Marsden identity for quantum Bernstein bases is shown to be equivalent to the Pfaff-Saalsch?tz formula for hypergeometric series. The equivalence of the q-versions of these formulas and identities is also demonstrated.

Lifting construction based on Bernstein bases and application in image compression

2010 ◽  
Vol 4 (5) ◽  
pp. 385 ◽  
Author(s):  
X. Yang ◽  
Z. Zhu ◽  
Y. Guo ◽  
Z. Quan
Keyword(s):  
Image Compression ◽  
Bernstein Bases
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