Approximation of multivariate function by using new multivariate Bernstein α-polynomials

In this paper the approximation of multivariate function by using multivariate Bernstein α-polynomials is considered. The Bernstein α-polynomials are given and an identity is constructed. With these the well-known multivariate Bernstein approximation is expanded. The main result is for any continuou...

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Veröffentlicht in:Applied mathematics and computation Jg. 154; H. 2; S. 335 - 345
Hauptverfasser: Hou, Zai-En, Zhang, Ke-Cun
Format: Journal Article
Sprache:Englisch
Veröffentlicht: New York, NY Elsevier Inc 05.07.2004
Elsevier
Schlagworte:
Acceleration of convergence
Approximation
Bernstein polynomial
Exact sciences and technology
Mathematics
Multivariate function
Numerical analysis
Numerical analysis. Scientific computation
Numerical approximation
Sciences and techniques of general use
Multivariate function
65B05
Approximation
65D15
Bernstein polynomial
Numerical approximation
Numerical analysis
Applied mathematics
N variable function
Continuous function
Function approximation
ISSN:0096-3003, 1873-5649
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Zusammenfassung:In this paper the approximation of multivariate function by using multivariate Bernstein α-polynomials is considered. The Bernstein α-polynomials are given and an identity is constructed. With these the well-known multivariate Bernstein approximation is expanded. The main result is for any continuous multivariate function f( x) there exist Bernstein α-polynomials {B n (f, x,α)} n which converge to f( x) uniformly on a box set as n→∞.
ISSN:0096-3003
1873-5649
DOI:10.1016/S0096-3003(03)00711-2