共查询到20条相似文献,搜索用时 62 毫秒
1.
一类Bernstein型算子加权逼近 总被引:3,自引:1,他引:2
本文首先给出了一类用递归法定义的Bernsein型算子在一致逼近意义下的特征刻划,然后指出在通常的加权范数下,它虹无界的,通过引入的一种新范数,我们给出了该算子加Jacobi权逼近的特征刻划。 相似文献
2.
研究了优势关系下不协调决策表的下近似约简问题,引入新的下近似约简的定义,证明新的下近似约简与文献[7]定义的下近似约简等价。给出新的下近似约简的判定定理和辨识矩阵,与文献[7]的辨识矩阵相比,计算新的下近似约简的辨识矩阵的时间复杂度要低。因此,可以利用新的辨识矩阵来求决策表的下近似约简. 相似文献
3.
We study various approximation classes associated with m-term approximation by
elements from a (possibly redundant) dictionary in a Banach space. The standard approximation
class associated with the best m-term approximation is compared to new classes defined by
considering m-term approximation with algorithmic constraints: thresholding and Chebychev approximation
classes are studied, respectively. We consider embeddings of the Jackson type (direct
estimates) of sparsity spaces into the mentioned approximation classes. General direct estimates
are based on the geometry of the Banach space, and we prove that assuming a certain structure of
the dictionary is sufficient and (almost) necessary to obtain stronger results. We give examples of
classical dictionaries in Lp spaces and modulation spaces where our results recover some known
Jackson type estimates, and discuss some new estimates they provide. 相似文献
4.
We show that the existence of a martingale approximation of a stationary process depends on the choice of the filtration. There exists a stationary linear process which has a martingale approximation with respect to the natural filtration, but no approximation with respect to a larger filtration with respect to which it is adapted and regular. There exists a stationary process adapted, regular, and having a martingale approximation with respect to a given filtration but not (regular and having a martingale approximation) with respect to the natural filtration. 相似文献
5.
6.
Tsogtgerel Gantumur 《Foundations of Computational Mathematics》2017,17(4):917-956
This paper concerns characterizations of approximation classes associated with adaptive finite element methods with isotropic h-refinements. It is known from the seminal work of Binev, Dahmen, DeVore and Petrushev that such classes are related to Besov spaces. The range of parameters for which the inverse embedding results hold is rather limited, and recently, Gaspoz and Morin have shown, among other things, that this limitation disappears if we replace Besov spaces by suitable approximation spaces associated with finite element approximation from uniformly refined triangulations. We call the latter spaces multievel approximation spaces and argue that these spaces are placed naturally halfway between adaptive approximation classes and Besov spaces, in the sense that it is more natural to relate multilevel approximation spaces with either Besov spaces or adaptive approximation classes, than to go directly from adaptive approximation classes to Besov spaces. In particular, we prove embeddings of multilevel approximation spaces into adaptive approximation classes, complementing the inverse embedding theorems of Gaspoz and Morin. Furthermore, in the present paper, we initiate a theoretical study of adaptive approximation classes that are defined using a modified notion of error, the so-called total error, which is the energy error plus an oscillation term. Such approximation classes have recently been shown to arise naturally in the analysis of adaptive algorithms. We first develop a sufficiently general approximation theory framework to handle such modifications, and then apply the abstract theory to second-order elliptic problems discretized by Lagrange finite elements, resulting in characterizations of modified approximation classes in terms of memberships of the problem solution and data into certain approximation spaces, which are in turn related to Besov spaces. Finally, it should be noted that throughout the paper we paid equal attention to both conforming and non-conforming triangulations. 相似文献
7.
Son Luu Nguyen 《Nonlinear Analysis: Real World Applications》2012,13(3):1170-1185
This work develops numerical approximation algorithms for solutions of stochastic differential equations with Markovian switching. The existing numerical algorithms all use a discrete-time Markov chain for the approximation of the continuous-time Markov chain. In contrast, we generate the continuous-time Markov chain directly, and then use its skeleton process in the approximation algorithm. Focusing on weak approximation, we take a re-embedding approach, and define the approximation and the solution to the switching stochastic differential equation on the same space. In our approximation, we use a sequence of independent and identically distributed (i.i.d.) random variables in lieu of the common practice of using Brownian increments. By virtue of the strong invariance principle, we ascertain rates of convergence in the pathwise sense for the weak approximation scheme. 相似文献
8.
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. 相似文献
9.
10.
《Communications in Nonlinear Science & Numerical Simulation》2010,15(9):2235-2244
In recent years piecewise affine (PWA) modeling has developed as an attractive tool for the approximation of various complex nonlinear systems. In spite of the wide application of PWA modeling, the optimal approximation of a continuous time nonlinear system with scalar functions by the minimum number of affine systems has not been addressed properly in literature. This paper deals with a fuzzy clustering based approach for the optimal PWA approximation of a class of continuous time nonlinear systems. The technique is based on the trade-off between increasing the approximation accuracy of the various nonlinear functions and simplifying the approximation by the minimum number of subsystems. As an application, the technique is utilized to obtain a PWA approximation of the glucose regulation system. Numerical simulations depicted that, for a given number of subsystems, the derived glucose regulation model provides an optimal approximation of the original nonlinear system. The model also provided some biological insight about the interactions involved in glucose regulation. 相似文献
11.
Reinhard Hochmuth 《PAMM》2003,3(1):446-449
Restricted nonlinear approximation is a generalization of n‐term approximation in which a weight function is used to control the terms of the approximant. Here, restricted nonlinear approximation is considered with respect to anisotropic wavelet bases. In particular, characterizations for those functions, which provide a specific convergence rate by restricted nonlinear approximation, are presented. 相似文献
12.
结合最佳m项逼近和单边逼近的思想引进所谓最佳m项单边逼近的概念,给出由Fourier系数确定的光滑函数类通过三角函数系在Lp(1≤P≤∞)的最佳m-项单边逼近渐近估计以及m-项类贪婪单边逼近结果. 相似文献
13.
Daniel Vera 《Mathematische Nachrichten》2019,292(1):195-210
Restricted non linear approximation is a generalization of the N‐term approximation in which a measure on the index set of the approximants controls the type, instead of the number, of elements in the approximation. Thresholding is a well‐known type of non linear approximation. We relate a generalized upper and lower Temlyakov property with the decreasing rate of the thresholding approximation. This relation is in the form of a characterization through some general discrete Lorentz spaces. Thus, not only we recover some results in the literature but find new ones. As an application of these results, we compress and reduce noise of some images with wavelets and shearlets and show, at least empirically, that the L2‐norm is not necessarily the best norm to measure the approximation error. 相似文献
14.
Jens L. Eftang Martin A. Grepl Anthony T. Patera Einar M. Rønquist 《Foundations of Computational Mathematics》2013,13(5):763-787
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. 相似文献
15.
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. 相似文献
16.
《Journal of Computational and Applied Mathematics》1987,18(1):93-105
For the approximation of functions, interpolation compromises approximation error for computational convenience. For a bounded interpolation operator the Lebesque inequality bounds the factor by which the interpolation differs from the best approximation available in the range of the operator. A comparable process for one-sided approximation is not readily apparent. Methods are suggested for the computationally economical construction of one-sided spline approximation to large classes of functions, and criteria for comparing such approximation operators are investigated. Since the operators are generally nonlinear the Lebesque inequality is invalidated as an aid for comparing with the best one-sided approximation in the range of the operator, but comparable inequalities are shown to exist in some cases. 相似文献
17.
In this paper, we consider approximation algorithms for optimizing a generic multi-variate homogeneous polynomial function,
subject to homogeneous quadratic constraints. Such optimization models have wide applications, e.g., in signal processing,
magnetic resonance imaging (MRI), data training, approximation theory, and portfolio selection. Since polynomial functions
are non-convex, the problems under consideration are all NP-hard in general. In this paper we shall focus on polynomial-time
approximation algorithms. In particular, we first study optimization of a multi-linear tensor function over the Cartesian
product of spheres. We shall propose approximation algorithms for such problem and derive worst-case performance ratios, which
are shown to be dependent only on the dimensions of the model. The methods are then extended to optimize a generic multi-variate
homogeneous polynomial function with spherical constraint. Likewise, approximation algorithms are proposed with provable approximation
performance ratios. Furthermore, the constraint set is relaxed to be an intersection of co-centered ellipsoids; namely, we
consider maximization of a homogeneous polynomial over the intersection of ellipsoids centered at the origin, and propose
polynomial-time approximation algorithms with provable worst-case performance ratios. Numerical results are reported, illustrating
the effectiveness of the approximation algorithms studied. 相似文献
18.
证明了具有单一隐层的神经网络在L_ω~q的逼近,获得了网络逼近的上界估计和下界估计.这一结果揭示了神经网络在加权逼近的意义下,网络的收敛阶与隐层单元个数之间的关系,为神经网络的应用提供了重要的理论基础. 相似文献
19.
Lidong Wang Xiaodong LiuWangren Qiu 《International Journal of Approximate Reasoning》2012,53(2):200-211
The approximation space model was originally proposed by Pawlak (1982) [19]. It was Or?owska who first observed that approximation spaces serves as a formal counterpart of perception, or observation [16, §2, p. 8], in which approximations provide a means of approximating one set of objects with another set of objects using the indiscernibility relation. Topology has been used to enrich the original model of an approximation space as well as more recent models of generalized approximation spaces. In this paper, an extension of th e topology neighborhood based on AFS (Axiomatic Fuzzy Sets) theory is introduced, and some interesting properties are given. Furthermore, a new generalized approximation space model is established with two application examples, which can be used to deal with information tables with many category features and viewed as a multi-granulations form of nearness approximation space models. 相似文献
20.
Xu Shusheng 《分析论及其应用》1991,7(4):76-92
Let R be a normed linear space, K be an arbitrary convex subset of an n-dimensional subspace Φ
n
⊂R. This paper first gives a general charactaerization for a best approximation from K in form of “zero in the convex hull”.
Applying it to the uniform approximation by generalized polynomials with restricted ranges, we get further an alternation
characterization. Our results ocntains the special cases of interpolatory approximation, positive approximation, copositive
approximation, and the classical characterizations in forms of convex hull and alternation in approximation without restriction. 相似文献