共查询到20条相似文献,搜索用时 46 毫秒
1.
In this paper we introduce some new sequences of positive linear operators, acting on a sufficiently large space of continuous functions on the real line, which generalize Gauss–Weierstrass operators.We study their approximation properties and prove an asymptotic formula that relates such operators to a second order elliptic differential operator of the form Lu?αu′′+βu′+γu.Shape-preserving and regularity properties are also investigated. 相似文献
2.
We prove that a convex functionf ∈ L
p[−1, 1], 0<p<∞, can be approximated by convex polynomials with an error not exceeding Cω
3
ϕ
(f,1/n)p where ω
3
ϕ
(f,·) is the Ditzian-Totik modulus of smoothness of order three off. We are thus filling the gap between previously known estimates involving ω
3
ϕ
(f,1/n)p, and the impossibility of having such estimates involving ω4. We also give similar estimates for the approximation off by convexC
0 andC
1 piecewise quadratics as well as convexC
2 piecewise cubic polynomials.
Communicated by Dietrich Braess 相似文献
3.
J. Yoon 《Constructive Approximation》2001,17(2):227-247
A new multivariate approximation scheme on R
d
using scattered translates of the “shifted” surface spline function is developed. The scheme is shown to provide spectral
L
p
-approximation orders with 1 ≤ p ≤ ∞, i.e., approximation orders that depend on the smoothness of the approximands. In addition, it applies to noisy data
as well as noiseless data. A numerical example is presented with a comparison between the new scheme and the surface spline
interpolation method. 相似文献
4.
K. A. Kopotun 《Constructive Approximation》2001,17(2):307-317
One of the main results of this paper is the following Whitney theorem of interpolatory type for k-monotone functions (i.e., functions f such that divided differences f[x
0,…, x
k
] are nonnegative for all choices of (k + 1) distinct points x
0,…, x
k
. 相似文献
5.
We prove that a convex functionf C[–1, 1] can be approximated by convex polynomialsp
n
of degreen at the rate of 3(f, 1/n). We show this by proving that the error in approximatingf by C2 convex cubic splines withn knots is bounded by 3(f, 1/n) and that such a spline approximant has anL
third derivative which is bounded by n33(f, 1/n). Also we prove that iff C2[–1, 1], then it is approximable at the rate ofn
–2 (f, 1/n) and the two estimates yield the desired result.Communicated by Ronald A. DeVore. 相似文献
6.
B. J. C. Baxter 《Constructive Approximation》1991,7(1):427-440
In [4], deep results were obtained concerning the invertibility of matrices arising from radial basis function interpolation. In particular, the Euclidean distance matrix was shown to be invertible for distinct data. In this paper, we investigate the invertibility of distance matrices generated byp-norms. In particular, we show that, for anyp(1, 2), and for distinct pointsx
1,,x
n
d
, wheren andd may be any positive integers, with the proviso thatn2, the matrixA
n×n
defined by
相似文献
7.
Summary Forn=1, 2, 3, ..., let
n
denote the Lebesgue constant for Lagrange interpolation based on the equidistant nodesx
k, n
=k, k=0, 1, 2, ...,n. In this paper an asymptotic expansion for log
n
is obtained, thereby improving a result of A. Schönhage. 相似文献
8.
M. J. Johnson 《Constructive Approximation》1997,13(2):155-176
An upper bound on theL
p-approximation power (1 ≤p ≤ ∞) provided by principal shift-invariant spaces is derived with only very mild assumptions on the generator. It applies
to both stationary and nonstationary ladders, and is shown to apply to spaces generated by (exponential) box splines, polyharmonic
splines, multiquadrics, and Gauss kernel. 相似文献
9.
We prove a direct theorem for shape preservingL
p
-approximation, 0p, in terms of the classical modulus of smoothnessw
2(f, t
p
1
). This theorem may be regarded as an extension toL
p
of the well-known pointwise estimates of the Timan type and their shape-preserving variants of R. DeVore, D. Leviatan, and X. M. Yu. It leads to a characterization of monotone and convex functions in Lipschitz classes (and more general Besov spaces) in terms of their approximation by algebraic polynomials.Communicated by Ron DeVore. 相似文献
10.
《Quaestiones Mathematicae》2013,36(2):157-165
Abstract The purpose of this paper is to relate the continuity and selection properties of the one-sided best uniform approximation operator to similar properties of the metric projection. Let M be a closed subspace of C(T) which contains constants. Then the one-sided best uniform approximation operator is Hausdorff continuous (resp. Lipschitz continuous) on C(T) if and only if the metric projection PM is Haudorff continuous (resp. Lipschitz continuous) on C(T). Also, the metric projection PM admits a continuous (resp. Lipschitz continuous) selection if and only if the one-sided best uniform approximation operator admits a continuous (resp. Lipschitz continuous) selection. 相似文献
11.
In this paper we give a complete expansion formula for Bernstein polynomials defined on ans-dimensional simplex. This expansion for a smooth functionf represents the Bernstein polynomialB
n
(f) as a combination of derivatives off plus an error term of orderO(n–s
).Communicated by Wolfgang Dahmen. 相似文献
12.
Rémi Arcangéli María Cruz López de Silanes Juan José Torrens 《Numerische Mathematik》2007,107(2):181-211
Given a function f on a bounded open subset Ω of with a Lipschitz-continuous boundary, we obtain a Sobolev bound involving the values of f at finitely many points of . This result improves previous ones due to Narcowich et al. (Math Comp 74, 743–763, 2005), and Wendland and Rieger (Numer
Math 101, 643–662, 2005). We then apply the Sobolev bound to derive error estimates for interpolating and smoothing (m, s)-splines. In the case of smoothing, noisy data as well as exact data are considered. 相似文献
13.
The main result proved in the paper is: iff is absolutely continuous in (–, ) andf' is in the real Hardy space ReH
1, then
for everyn1, whereR
n(f) is the best uniform approximation off by rational functions of degreen. This estimate together with the corresponding inverse estimate of V. Russak [15] provides a characterization of uniform rational approximation.Communicated by Ronald A. DeVore. 相似文献
14.
Erich van Wickeren 《Constructive Approximation》1989,5(1):189-198
Equivalence theorems concerning the convergence of the Bernstein polynomialsB
n
f are well known for continuous functionsf in the sup-norm. The purpose of this paper is to extend these results for functionsf, Riemann integrable on [0, 1], We have therefore to consider the seminorm
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