K-functionals and multivariate Bernstein polynomials
نویسندگان
چکیده
This paper estimates upper and lower bounds for the approximation rates of iterated Boolean sums of multivariate Bernstein polynomials. Both direct and inverse inequalities for the approximation rate are established in terms of a certain K -functional. From these estimates, one can also determine the class of functions yielding optimal approximations to the iterated Boolean sums. c © 2008 Elsevier Inc. All rights reserved.
منابع مشابه
The weighted dual functionals for the univariate Bernstein basis
We find an explicit formula for the weighted dual functions of the Bernstein polynomials with respect to the Jacobi weight function using the usual inner product in the Hilbert space L[0,1]. We define the weighted dual functionals of the Bernstein polynomials, which are used to find the coefficients in the least squares approximation. 2006 Elsevier Inc. All rights reserved.
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ورودعنوان ژورنال:
- Journal of Approximation Theory
دوره 155 شماره
صفحات -
تاریخ انتشار 2008