✦ LIBER ✦

A Note on Approximation by Bernstein Polynomials

✍ Scribed by T.F. Xie; S.P. Zhou

Publisher: Elsevier Science
Year: 1993
Tongue: English
Weight: 161 KB
Volume: 179
Category: Article
ISSN: 0022-247X
DOI: 10.1006/jmaa.1993.1352

No coin nor oath required. For personal study only.

✦ Synopsis

By establishing an identity for (S_{n}(x):=\sum_{j=0}^{n}|j / n-x|\left({ }{j}^{n}\right) x^{j}(1-x)^{n-j}), the present paper shows that a pointwise asymptotic estimate cannot hold for (S{n}(x)), and, at the same time, obtains a better result than that in Bojanic and Cheng [3]. 1993 Academic Press, Inc.

📜 SIMILAR VOLUMES

A Note on Derivatives of Bernstein Polyn

A Note on Derivatives of Bernstein Polynomials

✍ D.X. Zhou 📂 Article 📅 1994 🏛 Elsevier Science 🌐 English ⚖ 92 KB

Another Note on Polynomial vs Rational A

Another Note on Polynomial vs Rational Approximation

✍ Boris Shekhtman 📂 Article 📅 1996 🏛 Elsevier Science 🌐 English ⚖ 221 KB

Let E be a subspace of C(X) and let R(E)= gÂh: g, h # E ; h>0]. We make a simple, yet intriguing observation: if zero is a best approximation to f from E, then zero is a best approximation to f from R(E ). We also prove that if That extends the results of P. Borwein and S. Zhou who proved it for t

A Note on Weighted Polynomial Approximat

A Note on Weighted Polynomial Approximation with Varying Weights

✍ A.B.J. Kuijlaars 📂 Article 📅 1996 🏛 Elsevier Science 🌐 English ⚖ 199 KB

It is shown that if weighted polynomials w n P n with deg P n n converge uniformly on the support of the extremal measure associated with w, then they converge to 0 everywhere else. It is also shown that uniform approximation on the support can always be characterized by a closed subset Z having the

A Note on Bernstein′s Theorems

✍ J. Lithner; A.P. Wojcik 📂 Article 📅 1995 🏛 Elsevier Science 🌐 English ⚖ 216 KB

A Note on Polynomial Reduction

✍ Alyson Reeves; Bernd Sturmfels 📂 Article 📅 1993 🏛 Elsevier Science 🌐 English ⚖ 137 KB

The reduction relation modulo a marked set of polynomials is Noetherian if and only if the marking is induced from an admissible term order.

Variation Diminishing Properties of Bern

Variation Diminishing Properties of Bernstein Polynomials on a Tetrahedron

✍ A. Bhatt; A. Ojha 📂 Article 📅 1994 🏛 Elsevier Science 🌐 English ⚖ 269 KB

Goodman has recently studied certain variation diminishing properties of Bernstein polynomials on triangles. Introducing analogous definitions for the variation of a trivariate function, we study in the present paper corresponding results for the Bernstein polynomials defined on a tetrahedron. We ha