Open AccessNearly monotone spline approximation in 𝕃_{𝕡}
Author(s) -
Kirill A. Kopotun,
D. Leviatan,
Andriy Prymak
Publication year - 2005
Publication title -
proceedings of the american mathematical society
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.968
H-Index - 84
eISSN - 1088-6826
pISSN - 0002-9939
DOI - 10.1090/s0002-9939-05-08365-6
Subject(s) - algorithm , artificial intelligence , computer science , mathematics
It is shown that the rate of L p \mathbb {L}_p -approximation of a non-decreasing function in L p \mathbb {L}_p , 0 > 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.