基于比例移动最小二乘近似的误差分析

相较于移动最小二乘近似方法,比例移动最小二乘近似法有效地克服了前者带来的矩阵病态这一问题,展示出了更好的数值稳定性和更高的计算精度.给出了比例移动最小二乘近似对函数及其任意阶导数的误差估计,并给出了数值算例来验证之前的理论分析结果,通过与移动最小二乘近似的比较,表明比例移动最小二乘近似能得到更快的收敛性和更稳定的计算性.     

Continued fraction approximation for the Gamma function based on the Tri-gamma function

In this paper, we present a continued fraction product approximation for the Gamma function, via the Tri-gamma function. This approximation is fast in comparison with the recently discovered asymptotic series. We also establish the inequalities related to this approximation. Finally, some numerical computations are provided for demonstrating the superiority of our approximation.     

关于苏联科学院数学研究所在函数逼近论方面的工作（下）

关于苏联科学院数学研究所在函数逼近论方面的工作（下）ＣＡ．捷里亚可夫斯基（原苏联科学院数学研究所）６多元函数逼近多元函数逼近的正逆定理最早是由Ｄ．Ｊａｃｋｓｏｎ［４］和Ｓ．Ｎ．Ｂｅｒｎｓｔｅｉｎ［５］与一元函数的定理同时给出的，对多元函数的系统研究要...     

Analysis of the complex moving least squares approximation and the associated element-free Galerkin method

The complex moving least squares approximation is an efficient method to construct approximation functions in meshless methods. This paper begins by analyzing properties, stability and error of the approximation. To overcome the inherent instability, a stabilized approximation is also developed and analyzed. The complex element-free Galerkin method is a meshless method combined with the use of the complex moving least squares approximation. Application of the complex element-free Galerkin method to linear and nonlinear time-dependent problems is then given. Error estimates of the complex element-free Galerkin method are derived theoretically. Numerical examples involving function fitting and solitons are finally provided to show the accuracy and efficiency of the proposed methods.     

Lagrange插值在—重积分Wiener空间下的同时逼近平均误差

在加权L_p范数逼近意义下,确定了基于扩充的第二类Chebyshev结点组的Lagrange插值多项式列,在一重积分Wiener空间下同时逼近平均误差的渐近阶.结果显示,在L_p范数逼近意义下,Lagrange插值多项式列逼近函数及其导数的平均误差都弱等价于相应的最佳逼近多项式列的平均误差.同时,在信息基复杂性的意义下,若可允许信息泛函为标准信息,则上述插值算子列逼近函数及其导数的平均误差均弱等价于相应的最小非自适应信息半径.     

Saddlepoint Approximations to the Probability of Ruin in Finite Time for the Compound Poisson Risk Process Perturbed by Diffusion

A large deviations type approximation to the probability of ruin within a finite time for the compound Poisson risk process perturbed by diffusion is derived. This approximation is based on the saddlepoint method and generalizes the approximation for the non-perturbed risk process by Barndorff-Nielsen and Schmidli (Scand Actuar J 1995(2):169–186, 1995). An importance sampling approximation to this probability of ruin is also provided. Numerical illustrations assess the accuracy of the saddlepoint approximation using importance sampling as a benchmark. The relative deviations between saddlepoint approximation and importance sampling are very small, even for extremely small probabilities of ruin. The saddlepoint approximation is however substantially faster to compute.     

On the de la Vallée-Poussin Means on the Sphere

We study the approximation behavior of the de la Vallée-Poussin means on the sphere. To do so, we establish relations between the means and the best approximation, and estimate the rate of convergence of the means by various moduli of smoothness. We also discuss the related approximation problem for zonal functions.     

An approximation algorithm for the traveling tournament problem

This paper describes the traveling tournament problem, a well-known benchmark problem in the field of tournament timetabling. We propose a new lower bound for the traveling tournament problem, and construct a randomized approximation algorithm yielding a feasible solution whose approximation ratio is less than 2+(9/4)/(n−1), where n is the number of teams. Additionally, we propose a deterministic approximation algorithm with the same approximation ratio using a derandomization technique. For the traveling tournament problem, the proposed algorithms are the first approximation algorithms with a constant approximation ratio, which is less than 2+3/4.     

Approximation of Parametric Derivatives by the Empirical Interpolation Method

We introduce a general a priori convergence result for the approximation of parametric derivatives of parametrized functions. We consider the best approximations to parametric derivatives in a sequence of approximation spaces generated by a general approximation scheme, and we show that these approximations are convergent provided that the best approximation to the function itself is convergent. We also provide estimates for the convergence rates. We present numerical results with spaces generated by a particular approximation scheme—the Empirical Interpolation Method—to confirm the validity of the general theory.     

Influence of the approximation viscosity on the numerical solution of the problem on the accretion disk in a binary star system

We study the effect of the approximation viscosity of Godunov-type difference schemes in a model problem on the accretion disk in a binary star system. Computations are carried out by schemes of the first and increased approximation order. In the higher-order scheme, we take into account the viscous stress tensor, which is used to model the influence of the approximation viscosity observed in the first-order scheme. It is noteworthy that the approximation viscosity can lead to global qualitative changes in the flows to be modeled. The numerical results given in the paper are of independent interest in that they illustrate some new specific features of gasdynamic flows in this classical problem of modern astrophysics.     

Edgeworth expansion for the survival function estimator in the Koziol-Green model

In the Koziol-Green or proportional hazards random censorship model, the asymptotic accuracy of the estimated one-term Edgeworth expansion and the smoothed bootstrap approximation for the Studentized Abdushukurov-Cheng-Lin estimator is investigated. It is shown that both the Edgeworth expansion estimate and the bootstrap approximation are asymptotically closer to the exact distribution of the Studentized Abdushukurov-Cheng-Lin estimator than the normal approximation.     

A Multinomial Approximation Approach for the Finite Time Survival Probability Under the Markov-modulated Risk Model

In this paper, we consider the problem of computing different types of finite time survival probabilities for a Markov-Modulated risk model and a Markov-Modulated risk model with reinsurance, both with varying premium rates. We use the multinomial approximation scheme to derive an efficient recursive algorithm to compute finite time survival probabilities and finite time draw-down survival probabilities. Numerical results show that by comparing with MCMC approximation, discretize approximation and diffusion approximation methods, the proposed scheme performs accurate results in all the considered cases and with better computation efficiency.

     

模糊粗糙近似算子公理集的独立性

用双论域上的模糊关系定义了广义模糊粗糙近似算子,并讨论了近似算子的性质。用公理刻画了模糊集合值算子,各种公理化的近似算子可以保证找到相应的二元模糊关系,使得由模糊关系通过构造性方法定义的模糊粗糙近似算子恰好就是用公理定义的近似算子。讨论了刻画各种特殊近似算子的公理集的独立性,从而给出各种特殊模糊关系所对应的模糊粗糙近似算子的最小公理集。     

单隐层神经网络与最佳多项式逼近

研究单隐层神经网络逼近问题．以最佳多项式逼近为度量,用构造性方法估计单隐层神经网络逼近连续函数的速度．所获结果表明:对定义在紧集上的任何连续函数,均可以构造一个单隐层神经网络逼近该函数,并且其逼近速度不超过该函数的最佳多项式逼近的二倍．     

球面带形平移网络逼近的Jackson定理

研究了球面带型平移网络逼近阶用球面调和多项式的最佳逼近及光滑模的刻画问题．借助于球调和多项式的最佳逼近多项式和Riesz平均构造出了单位球面Sq上的带形平移网络,并建立了球面带形平移网络对Lp(Sq)中函数一致逼近的Jackson型定理．所得结果表明球面带形平移网络可以达到球调和多项式的逼近阶．     

Existence of Attractors for Approximations to the Bingham Model and Their Convergence to the Attractors of the Initial Model

Considering the Bingham fluid motion model, we study the approximation problem, prove its unique solvability, and the existence of attractors. We show that the attractors of the approximation problem converge to the attractors of the Bingham model in the sense of the Hausdorff semidistance in the corresponding metric space as the approximation parameter vanishes.

     

Polynomial approximation in Sobolev spaces on the unit sphere and the unit ball

This work is a continuation of the recent study by the authors on approximation theory over the sphere and the ball. The main results define new Sobolev spaces on these domains and study polynomial approximations for functions in these spaces, including simultaneous approximation by polynomials and the relation between the best approximation of a function and its derivatives.     

A new approximation operator of the Arato-Renyi type

In this paper a new approximation operator is introduced and its properties are studied. Special cases of this operator are the well-known Szàsz power-series approximation operator and its generalization by D. Leviatan. The behaviour of the new approximation operator at points of continuity and discontinuity is investigated by using probabilistic tools as the Chebishev inequality and Liapounov’s central limit theorem. Such probabilistic methods of proof simplify the proofs and give better understanding of the approximation mechanism.     

Approximation by Bézier variants of the BBHK operators

In this work a new type of approximation operator—the Bézier variant of the BBHK operator—is introduced. Its approximation properties are studied. A convergence theorem for such approximation operators for locally bounded functions is established by means of some techniques of probability theory and analysis methods. This convergence theorem subsumes the approximation of functions of bounded variation as a special case.     

The similarity between the best approximation and the best copositive approximation

In this paper the author studies the copositive approximation in C(?) by elements of finite dimensional Chebyshev subspaces in the general case when ? is any totally ordered compact space. He studies the similarity between me behavior of the ordinary best approximation and the behavior pf the copositive best approximation. At the end of this paper, the author isolates many cases at which the two behaviors are the same.