TY - JOUR
T1 - Nearly monotone spline approximation in double struck L signp
AU - Kopotun, K.
AU - Leviatan, D.
AU - Prymak, A. V.
PY - 2006/7
Y1 - 2006/7
N2 - It is shown that the rate of Lp-approximation of a non-decreasing function in double struck L signp, 0 < p < oc, 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.
AB - It is shown that the rate of Lp-approximation of a non-decreasing function in double struck L signp, 0 < p < oc, 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.
KW - Degree of approximation
KW - Jackson type estimates
KW - Monotone approximation by piecewise polynomials and splines
UR - http://www.scopus.com/inward/record.url?scp=33745964769&partnerID=8YFLogxK
U2 - 10.1090/S0002-9939-05-08365-6
DO - 10.1090/S0002-9939-05-08365-6
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AN - SCOPUS:33745964769
VL - 134
SP - 2037
EP - 2047
JO - Proceedings of the American Mathematical Society
JF - Proceedings of the American Mathematical Society
SN - 0002-9939
IS - 7
ER -