|
BEST LIPSCHITZ CONSTANTS FOR THE BÉZIER NETS AND BERNSTEIN POLYNOMIALS OVER A SIMPLEX
Chen Falai
Acta mathematica scientia,Series B. 1998, 18 (3):
262-270.
The present paper finds out that the geometric entity which characterizes the best Lipschitz constants for the Bézier nets and Bernstein polynomials over a simplex σ is an angle φ determined by σ, and proves that (1) if f(x) is Lipschitz continuous over σ, i.e., f(x) ∈ LipA(α,σ), then both the n-th Bézier net fn and the n-th Bernstein polynomial Bn(f; x) corresponding to f(x) belong to LipB(α,σ), where B=Asecαφ; and (2) if n-th Bézier net fn ∈ LipA(α,σ), then the elevation Bézier net Efn and the corresponding Bernstein polynomial Bn(f,;x) also belong to LipA(α,σ). Furthermore, the constant B=Asecαφ in case (1) is best in some sense.
Related Articles |
Metrics
|