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1.
In this paper, we study bootstrap approximation for generalizedU-processes (GUP) indexed by a class of functions. Under mild conditions we obtain that the asymptotic distributions of bootstrapping generalizedU-processes (BGUP) are the same as those of GUP almost surely. As a result, the asymptotic properties of bootstrap approximation for PP generalizedU-processes (BPPGUP) are obtained. In addition we have derived bootstrap approximation for generalizedV-processes (GVP). Thus, we can use BGUP or bootstrapping GVP (BGVP) to simulate GUP and GVP.This project is supported by the National Natural Science Foundation of China and the Science Foundation of Educational Committee of Guizhou. 相似文献
2.
In the univariate case there are certain equivalences between the
nonlinear approximation methods that use piecewise polynomials and
those that use rational functions. It is known that for certain
parameters the respective approximation spaces are identical and
may be described as Besov spaces. The characterization of the
approximation spaces of the multivariate nonlinear approximation
by piecewise polynomials and by rational functions is not known.
In this work we compare between the two methods in the bivariate
case. We show some relations between the approximation spaces of
piecewise polynomials defined on n triangles and those of
bivariate rational functions of total degree n which are
described by n parameters. Thus we compare two classes of
approximants with the same number Cn of parameters. We consider
this the proper comparison between the two methods. 相似文献
3.
In this paper, we study the pointwise approximation of functions defined on the real semiaxis and having an rth derivative bounded almost everywhere. The approximation is performed by means of entire functions of bounded half-degree, which were introduced by S. N. Bernstein. An asymptotically sharp estimate for pointwise approximation of this class of functions is obtained. 相似文献
4.
We study the problem of maximizing constrained non-monotone submodular functions and provide approximation algorithms that improve existing algorithms in terms of either the approximation factor or simplicity. Different constraints that we study are exact cardinality and multiple knapsack constraints for which we achieve (0.25−?)-factor algorithms.We also show, as our main contribution, how to use the continuous greedy process for non-monotone functions and, as a result, obtain a 0.13-factor approximation algorithm for maximization over any solvable down-monotone polytope. 相似文献
5.
Ruchi Ruchi Nurhayat Ispir P. N. Agrawal 《Mathematical Methods in the Applied Sciences》2017,40(16):5687-5706
Ren and Zeng (2013) introduced a new kind of q‐Bernstein–Schurer operators and studied some approximation properties. Acu et al. (2016) defined the Durrmeyer modification of these operators and studied the rate of convergence and statistical approximation. The purpose of this paper is to introduce a Kantorovich modification of these operators by using q‐Riemann integral and investigate the rate of convergence by means of the Lipschitz class and the Peetre's K‐functional. Next, we introduce the bivariate case of q‐Bernstein–Schurer–Kantorovich operators and study the degree of approximation with the aid of the partial modulus continuity, Lipschitz space, and the Peetre's K‐functional. Finally, we define the generalized Boolean sum operators of the q‐Bernstein–Schurer–Kantorovich type and investigate the approximation of the Bögel continuous and Bögel differentiable functions by using the mixed modulus of smoothness. Furthermore, we illustrate the convergence of the operators considered in the paper for the univariate case and the associated generalized Boolean sum operators to certain functions by means of graphics using Maple algorithms. Copyright © 2017 John Wiley & Sons, Ltd. 相似文献
6.
The main achievement of this paper is that we show, what was to us, a surprising conclusion, namely, twice continuously differentiable
functions in (0,1) (with some regular behavior at the endpoints) which change monotonicity at least once in the interval, are approximable
better by comonotone polynomials, than are such functions that are merely monotone. We obtain Jackson-type estimates for the
comonotone polynomial approximation of such functions that are impossible to achieve for monotone approximation.
July 7, 1998. Date revised: May 5, 1999. Date accepted: July 23, 1999. 相似文献
7.
We study two methods for solving a univariate Fredholm integral equation of the second kind, based on (left and right) partial
approximations of the kernel K by a discrete quartic spline quasi-interpolant. The principle of each method is to approximate the kernel with respect to
one variable, the other remaining free. This leads to an approximation of K by a degenerate kernel. We give error estimates for smooth functions, and we show that the method based on the left (resp.
right) approximation of the kernel has an approximation order O(h
5) (resp. O(h
6)). We also compare the obtained formulae with projection methods. 相似文献
8.
Dominik Schmid 《Numerical Functional Analysis & Optimization》2013,34(7-8):855-882
We consider scattered data approximation problems on SO(3). To this end, we construct a new operator for polynomial approximation on the rotation group. This operator reproduces Wigner-D functions up to a given degree and has uniformly bounded L p -operator norm for all 1 ≤ p ≤ ∞. The operator provides a polynomial approximation with the same approximation degree of the best polynomial approximation. Moreover, the operator together with a Markov type inequality for Wigner-D functions enables us to derive scattered data L p -Marcinkiewicz–Zygmund inequalities for these functions for all 1 ≤ p ≤ ∞. As a major application of such inequalities, we consider the stability of the weighted least squares approximation problem on SO(3). 相似文献
9.
Under some assumptions on a function F and its Fourier transform
we prove new estimates of best approximation of F by entire functions of exponential type σ in Lp(
), 1 ≤ p < 2. The proof is based on some inequalities for
in L1(
) which may be treated as generalizations of results of Bausov and Telyakovskii. As an application we obtain exact estimates of best approximation of some infinitely differentiable functions. 相似文献
10.
In this paper, we have obtained an approximation result in the Generalized Finite Element Method (GFEM) that reflects the
global approximation property of the Partition of Unity (PU) as well as the approximability of the local approximation spaces.
We have considered a GFEM, where the underlying PU functions reproduce polynomials of degree l. With the space of polynomials of degree k serving as the local approximation spaces of the GFEM, we have shown, in particular, that the energy norm of the GFEM approximation
error of a smooth function is O(h
l + k
). This result cannot be obtained from the classical approximation result of GFEM, which does not reflect the global approximation
property of the PU. 相似文献
11.
We consider approximation of L
p
functions by Hardy functions on subsets of the circle for . After some preliminaries on the possibility of such an approximation which are connected to recovery problems of the Carleman
type, we prove existence and uniqueness of the solution to a generalized extremal problem involving norm constraints on the
complementary subset.
December 6, 1995. Date revised: August 26, 1996. 相似文献
12.
Summary. In this paper we develop an efficient Schur complement method for solving the 2D Stokes equation. As a basic algorithm, we
apply a decomposition approach with respect to the trace of the pressure. The alternative stream function-vorticity reduction
is also discussed. The original problem is reduced to solving the equivalent boundary (interface) equation with symmetric
and positive definite operator in the appropriate trace space. We apply a mixed finite element approximation to the interface
operator by
iso
triangular elements and prove the optimal error estimates in the presence of stabilizing bubble functions. The norm equivalences
for the corresponding discrete operators are established. Then we propose an asymptotically optimal compression technique
for the related stiffness matrix (in the absence of bubble functions) providing a sparse factorized approximation to the Schur
complement. In this case, the algorithm is shown to have an optimal complexity of the order , q = 2 or q = 3, depending on the geometry, where N is the number of degrees of freedom on the interface. In the presence of bubble functions, our method has the complexity
arithmetical operations. The Schur complement interface equation is resolved by the PCG iterations with an optimal preconditioner.
Received March 20, 1996 / Revised version received October 28, 1997 相似文献
13.
P. Oswald 《Journal of Mathematical Sciences》2008,155(1):109-128
In [9], we proved numerically that spaces generated by linear combinations of some two-dimensional Haar functions exhibit
unexpectedly nice orders of approximation for solutions of the single-layer potential equation in a rectangle. This phenomenon
is closely related, on the one hand, to the properties of the approximation method of hyperbolic crosses and on the other
to the existence of a strong singularity for solutions of such boundary integral equations. In the present paper, we establish
several results on the approximation for the hyperbolic crosses and on the best N-term approximations by linear combinations of Haar functions in the H
s
-norms, −1 < s < 1/2; this provides a theoretical base for our numerical research. To the author's best knowledge, the negative smoothness
case s < 0 was not studied earlier.
__________
Translated from Sovremennaya Matematika. Fundamental'nye Napravleniya (Contemporary Mathematics. Fundamental Directions),
Vol. 25, Theory of Functions, 2007. 相似文献
14.
Fuat Usta 《Numerical Methods for Partial Differential Equations》2021,37(1):782-795
The main motivation of this paper is to provide a generalization of Bernstein‐Chlodowsky type operators which depend on function τ by means of two sequences of functions. The newly defined operators fix the test function set {1, τ, τ2} . Then we present the approximation properties of newly defined operators, such as weighted approximation, degree of approximation and Voronovskaya type theorems. Finally, we present a series of numerical examples demonstrating the effectiveness of this newly defined Bernstein‐Chlodowsky operators for computing function approximation. 相似文献
15.
In this paper we consider best Chebyshev approximation to continuous functions by generalized rational functions using an optimization theoretical approach introduced in [[5.]]. This general approach includes, in a unified way, usual, weighted, one-sided, unsymmetric, and also more general rational Chebychev approximation problems with side-conditions. We derive various continuity conditions for the optimal value, for the feasible set, and the optimal set of the corresponding optimization problem. From these results we derive conditions for the upper semicontinuity of the metric projection, which include some of the results of Werner [On the rational Tschebyscheff operator, Math. Z. 86 (1964), 317–326] and Cheney and Loeb [On the continuity of rational approximation operators, Arch. Rational Mech. Anal. 21 (1966), 391–401]. 相似文献
16.
Fatma Taşdelen Ali Olgun Gülen Başcanbaz-Tunca 《Proceedings Mathematical Sciences》2007,117(3):387-399
We introduce certain linear positive operators and study some approximation properties of these operators in the space of
functions, continuous on a compact set, of two variables. We also find the order of this approximation by using modulus of
continuity. Moreover we define an rth order generalization of these operators and observe its approximation properties. Furthermore, we study the convergence
of the linear positive operators in a weighted space of functions of two variables and find the rate of this convergence using
weighted modulus of continuity. 相似文献
17.
We study best uniform approximation of periodic functions from
where the kernelK(x, y) is strictly cyclic variation diminishing, and related problems including periodic generalized perfect splines. For various approximation problems of this type, we show the uniqueness of the best approximation and characterize the best approximation by extremal properties of the error function. The results are proved by using a characterization of best approximants from quasi-Chebyshev spaces and certain perturbation results. 相似文献
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18.
We study the multivariate approximation by certain partial sums (hyperbolic wavelet sums) of wavelet bases formed by tensor
products of univariate wavelets. We characterize spaces of functions which have a prescribed approximation error by hyperbolic
wavelet sums in terms of a K -functional and interpolation spaces. The results parallel those for hyperbolic trigonometric cross approximation of periodic
functions [DPT].
October 16, 1995. Date revised: August 28, 1996. 相似文献
19.
Frank Wikström 《Arkiv f?r Matematik》2001,39(1):181-200
We study different classes of Jensen measures for plurisubharmonic functions, in particular the relation between Jensen measures
for continuous functions and Jensen measures for upper bounded functions. We prove an approximation theorem for plurisubharmonic
functions inB-regular domain. This theorem implies that the two classes of Jensen measures coincide inB-regular domains. Conversely we show that if Jensen measures for continuous functions are the same as Jensen measures for
upper bounded functions and the domain is hyperconvex, the domain satisfies the same approximation theorem as above.
The paper also contains a characterisation in terms of Jensen measures of those continuous functions that are boundary values
of a continuous plurisubharmonic function. 相似文献
20.
Near Best Tree Approximation 总被引:2,自引:0,他引:2
Baraniuk R.G. DeVore R.A. Kyriazis G. Yu X.M. 《Advances in Computational Mathematics》2002,16(4):357-373
Tree approximation is a form of nonlinear wavelet approximation that appears naturally in applications such as image compression and entropy encoding. The distinction between tree approximation and the more familiar n-term wavelet approximation is that the wavelets appearing in the approximant are required to align themselves in a certain connected tree structure. This makes their positions easy to encode. Previous work [4,6] has established upper bounds for the error of tree approximation for certain (Besov) classes of functions. This paper, in contrast, studies tree approximation of individual functions with the aim of characterizing those functions with a prescribed approximation error. We accomplish this in the case that the approximation error is measured in L
2, or in the case p2, in the Besov spaces B
p
0(L
p
), which are close to (but not the same as) L
p
. Our characterization of functions with a prescribed approximation order in these cases is given in terms of a certain maximal function applied to the wavelet coefficients. 相似文献