ISSN:
1432-0940
Keywords:
Bernstein-Schoenberg operator
;
Bernstein polynomial
;
MultivariateB-spline
;
Asymptotic error
;
41A15
;
41A63
Source:
Springer Online Journal Archives 1860-2000
Topics:
Mathematics
Notes:
Abstract The bivariate Bernstein-Schoenberg operatorV T of degreem, introduced in [5], is a spline approximation operator that generalizes the Bernstein polynomial operatorB m . It is shown here that for a convex functionf,f≤V T (f)≤B m (f). This result is then used to show that for a twice differentiable functiong, the asymptotic error limm(V T (g)-g) depends only on the asymptotic error for quadratic polynomials. The latter is evaluated explicitly in the special circumstances thatV T is, in a sense, asymptotically close toB m .
Type of Medium:
Electronic Resource
URL:
http://dx.doi.org/10.1007/BF01890558
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