Characterization of Periodic L1-Unicity Subspaces

We are interested in characterizing the finite-dimensional subspaces of periodic, real-valued, and continuous functions which admit uniqueness of weighted best L¹-approximations. Considering the cases of odd and even dimension separately, we are able to give intrinsic characterizations of periodic L¹-unicity subspaces.     

Extended Best Polynomial Approximation Operator in Orlicz Spaces

In this article we consider the best polynomial approximation operator, defined in an Orlicz space L ^Φ(B), and its extension to L ^?(B) where ? is the derivative function of Φ. A characterization of these operators and several properties are obtained.     

复赋范空间中的同时太阳集的最佳逼近

研究了复赋范空间中的同时太阳集对无穷序列的最佳逼近问题，得到了特征及唯一性定理．     

Best uniform approximation to a class of rational functions

We explicitly determine the best uniform polynomial approximation to a class of rational functions of the form 1/²(x−c)+K(a,b,c,n)/(x−c) on [a,b] represented by their Chebyshev expansion, where a, b, and c are real numbers, n−1 denotes the degree of the best approximating polynomial, and K is a constant determined by a, b, c, and n. Our result is based on the explicit determination of a phase angle η in the representation of the approximation error by a trigonometric function. Moreover, we formulate an ansatz which offers a heuristic strategies to determine the best approximating polynomial to a function represented by its Chebyshev expansion. Combined with the phase angle method, this ansatz can be used to find the best uniform approximation to some more functions.     

广义权函数的最大类逼近及其应用

本文研究了广义权函数的最大类逼近问题,给出了K-最大类和A-最大类的特征刻划．同时也给出了关于广义权函数逼近的唯一性元特征刻划的结果和对某些具体逼近问题的应用,从而推广和改进了他人的结果．     

Distribution function estimates by Wasserstein metric and Bernstein approximation for C-1 functions

The aim of the paper is to estimate the density functions or distribution functions measured by Wasserstein metric, a typical kind of statistical distances, which is usually required in the statistical learningBased on the classical Bernstein approximation, a scheme is presented.To get the error estimates of the scheme, the problem turns to estimating the L1 norm of the Bernstein approximation for monotone C-1functions, which was rarely discussed in the classical approximation theoryFinally, we get a probability estimate by the statistical distance.     

Best Simultaneous L p -Approximation on Small Regions

In this article, we study the behavior of best simultaneous L ^p -approximation by algebraic polynomials on a union of intervals when the measure of them tend to zero. We also get an interpolation result.     

A result analogous to G. Szego’s theorem

The paper proves a new result similar to the well known theorems of G. Szego and A. Kolmogorov on the best approximation by analytic polynomials in weighted L ^p spaces. Such results are essential in prediction theory for stationary processes. It is well known, that for one step prediction, the size of the best approximation is the same for all p. The paper proves that for two step prediction the best approximation sizes are different for p = 2 and p = ∞.     

"Push-the-Error" Algorithm for Nonlinear n-Term Approximation

This paper is concerned with further developing and refining the analysis of a recent algorithmic paradigm for nonlinear approximation, termed the "Push-the-Error" scheme. It is especially designed to deal with L_∞-approximation in a multilevel framework. The original version is extended considerably to cover all commonly used multiresolution frameworks. The main conceptually new result is the proof of the quasi-semi-additivity of the functional N(ε) counting the number of terms needed to achieve accuracy ε. This allows one to show that the improved scheme captures all rates of best n-term approximation.     

Banach空间中太阳集对无穷序列的最佳同时逼近

本文研究太阳集对一列无穷序列的最佳同时逼近问题,建立了特征及唯一性结果．     

On Best Approximations from RS-sets in Complex Banach Spaces

The concept of an RS-set in a complex Banach space is introduced and the problem of best approximation from an RS-set in a complex space is investigated. Results consisting of characterizations, uniqueness and strong uniqueness are established,     

Linear best approximation using a class ofk-majorl p norms

Consideration is given to problems of linear best approximation using a variant of the usuall _p norms referred to ask-majorl _p norms, for the cases when 1<p<. The underlying problem is the minimization of a piecewise smooth function. Best approximations are characterized, and a descent algorithm is developed.     

The Best Multipoint Padé Approximant

Abstract

This paper is dealing with the problem of finding the “best” multipoint Padé approximant of an analytic function when data in some neighborhoods of sampling points are more important than others. More exactly, we obtain a multipoint Padé approximants as limits of best rational L^p-approximations on union of disks, when the measure of them tends to zero with different speeds. As such, this technique provides useful qualitative and analytic information concerning the approximants, which is difficult to obtain from a strictly numerical treatment.     

On the Discrete Poincaré–Friedrichs Inequalities for Nonconforming Approximations of the Sobolev Space H 1

We present a direct proof of the discrete Poincaré–Friedrichs inequalities for a class of nonconforming approximations of the Sobolev space H ¹(Ω), indicate optimal values of the constants in these inequalities, and extend the discrete Friedrichs inequality onto domains only bounded in one direction. We consider a polygonal domain Ω in two or three space dimensions and its shape-regular simplicial triangulation. The nonconforming approximations of H ¹(Ω) consist of functions from H ¹ on each element such that the mean values of their traces on interelement boundaries coincide. The key idea is to extend the proof of the discrete Poincaré–Friedrichs inequalities for piecewise constant functions used in the finite volume method. The results have applications in the analysis of nonconforming numerical methods, such as nonconforming finite element or discontinuous Galerkin methods.     

Boolean Functions with small Spectral Norm

Let be a boolean function, and suppose that the spectral norm of f is at most M. Then where and each H _j is a subgroup of . This result may be regarded as a quantitative analogue of the Cohen-Helson-Rudin structure theorem for idempotent measures in locally compact abelian groups. Received: May 2006 Accepted: January 2007     

Analysis of the M X /G/1 Queue Under D-Policy

Abstract

We study the queue length of the M ^X /G/1 queue under D-policy. We derive the queue length PGF at an arbitrary point of time. Then, we derive the mean queue length. As special cases, M/G/1, M ^X /M/1, and M/M/1 queue under D-policy are investigated. Finally, the effects of employing D-policy are discussed.     

Pointwise analog of the jackson approximation theorem

The pointwise version of the Jackson theorem on the best approximation by trigonometric polynomials is proved. Some application of the result is also presented.