Pointwise estimates for 3-monotone approximation

JOURNAL OF APPROXIMATION THEORY

卷:164

Article

Bondarenko, Andriy^2,3  Leviatan, Dany¹  Prymak, Andriy⁴ 

[1] Tel Aviv Univ, Raymond & Beverly Sackler Sch Math, IL-69978 Tel Aviv, Israel

[2] Ctr Recerca Matemat, Bellaterra 08193, Barcelona, Spain

[3] Natl Taras Shevchenko Univ, Dept Math Anal, UA-01033 Kiev, Ukraine

[4] Univ Manitoba, Dept Math, Winnipeg, MB R3T 2N2, Canada

关键词: Shape preserving approximation;    3-monotone approximation by piecewise polynomials and splines;    3-monotone polynomial approximation;    Degree of pointwise approximation;   

DOI  :  10.1016/j.jat.2012.06.002

来源: Elsevier

【 摘 要 】

We prove that for a 3-monotone function F is an element of C[-1, 1], one can achieve the pointwise estimates [F(x) - Psi(x)] <= c omega(3)(F.rho(n)(x)). x is an element of [-1,1] where rho(n)(x) := 1/n(2) + root 1-x(2)/n and c is an absolute constant, both with Psi, a 3-monotone quadratic spline on the nth Chebyshev partition, and with Psi, a 3-monotone polynomial of degree <= n. The basis for the construction of these splines and polynomials is the construction of 3-monotone splines, providing appropriate order of pointwise approximation, half of which nodes are prescribed and the other half are free, but controlled. (C) 2012 Elsevier Inc. All rights reserved.

【 授权许可】

Free