Nearly monotone spline approximation in $\mathbb {L}_p$
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- by K. Kopotun, D. Leviatan and A. V. Prymak PDF
- Proc. Amer. Math. Soc. 134 (2006), 2037-2047 Request permission
Abstract:
It is shown that the rate of $\mathbb {L}_p$-approximation of a non-decreasing function in $\mathbb {L}_p$, $0<p<\infty$, 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.References
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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
- 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
- © Copyright 2005
American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication. - Journal: Proc. Amer. Math. Soc. 134 (2006), 2037-2047
- MSC (2000): Primary 41A10, 41A25, 41A29
- DOI: https://doi.org/10.1090/S0002-9939-05-08365-6
- MathSciNet review: 2215773