منابع مشابه
Multivariate Bernstein polynomials and convexity
It is well known that in two or more variables Bernstein polynomi-als do not preserve convexity. Here we introduce two variations, one stronger than the classical notion, the other one weaker, which are preserved. Moreover, a weaker suucient condition for the monotony of subsequent Bernstein polynomials is given. linearly independent, in the course of which d has to be greater than or equal to ...
متن کاملK-functionals and multivariate Bernstein polynomials
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 Elsev...
متن کاملOn multivariate polynomials in Bernstein-Bézier form and tensor algebra
The Bernstein-Bézier representation of polynomials is a very useful tool in computer aided geometric design. In this paper we make use of (multilinear) tensors to describe and manipulate multivariate polynomials in their Bernstein-Bézier form. As application we consider Hermite interpolation with polynomials and splines.
متن کاملShape Restricted Nonparametric Regression Based on Multivariate Bernstein Polynomials
There has been increasing interest in estimating a multivariate regression function subject to shape restrictions, such as nonnegativity, isotonicity, convexity and concavity. The estimation of such shape-restricted regression curves is more challenging for multivariate predictors, especially for functions with compact support. Most of the currently available statistical estimation methods for ...
متن کاملOn Bernstein and Markov-Type Inequalities for Multivariate Polynomials on Convex Bodies
Let p n be a polynomial of m variables and total degree n such that & p n & C(K) =1, where K/R m is a convex body. In this paper we discuss some local and uniform estimates for the magnitude of grad p n under the above conditions. 1999 Academic Press Key Words: multivariate polynomials; convex bodies; gradient and directional derivative of polynomials.
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: Mathematics
سال: 2020
ISSN: 2227-7390
DOI: 10.3390/math8091397