Nearly monotone spline approximation in

Authors:
K. Kopotun, D. Leviatan and A. V. Prymak

Journal:
Proc. Amer. Math. Soc. **134** (2006), 2037-2047

MSC (2000):
Primary 41A10, 41A25, 41A29

Published electronically:
December 19, 2005

MathSciNet review:
2215773

Full-text PDF Free Access

Abstract | References | Similar Articles | Additional Information

Abstract: It is shown that the rate of -approximation of a non-decreasing function in , , by ``nearly non-decreasing" splines can be estimated in terms of the third classical modulus of smoothness (for uniformly spaced knots) and third Ditzian-Totik modulus (for Chebyshev knots), and that estimates in terms of higher moduli are impossible. It is known that these estimates are no longer true for ``purely" monotone spline approximation, and properties of intervals where the monotonicity restriction can be relaxed in order to achieve better approximation rate are investigated.

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Additional Information

**K. Kopotun**

Affiliation:
Department of Mathematics, University of Manitoba, Winnipeg, Manitoba, Canada R3T 2N2

Email:
kopotunk@cc.umanitoba.ca

**D. Leviatan**

Affiliation:
School of Mathematical Sciences, Raymond and Beverley Sackler Faculty of Exact Sciences, Tel Aviv University, Tel Aviv, 69978, Israel

Email:
leviatan@post.tau.ac.il

**A. V. Prymak**

Affiliation:
Faculty of Mechanics and Mathematics, National Taras Shevchenko University of Kyiv, Kyiv, 01033, Ukraine

Email:
prymak@univ.kiev.ua

DOI:
http://dx.doi.org/10.1090/S0002-9939-05-08365-6

Keywords:
Monotone approximation by piecewise polynomials and splines,
degree of approximation,
Jackson type estimates

Received by editor(s):
February 11, 2005

Published electronically:
December 19, 2005

Additional Notes:
The first author was supported in part by NSERC of Canada.

Part of this work was done while the third author visited Tel Aviv University in May 2004

Communicated by:
Jonathan M. Borwein

Article copyright:
© Copyright 2005
American Mathematical Society

The copyright for this article reverts to public domain 28 years after publication.