检索结果-内蒙古大学图书馆

approximation error estimates by noise-injected neural networks

MATHEMATICAL METHODS IN THE APPLIED SCIENCES 2024年第18期47卷 14563-14574页

作者： Akiyama, Keito Tohoku Univ Math Inst 6-3 Aramaki Aza AobaAoba Ku Sendai 9808578 Japan

One-hidden-layer feedforward neural networks are described as functions having many real-valued parameters. approximation properties of neural networks are established (universal approximation property), and the approximation error is related to the number of parameters in the network. The essentially optimal order of approximation error bounds was already derived in 1996. We focused on the numerical experiment that indicates the neural networks whose parameters contain stochastic perturbations gain better performance than ordinary neural networks and explored the approximation property of neural networks with stochastic perturbations. In this paper, we derived the quantitative order of variance of stochastic perturbations to achieve the essentially optimal approximation order and verified the justifiability of our theory by numerical experiments.

关键词： approximation of functions approximation order feedforward neural networks stochastic perturbations universal approximation property

来源：评论

学校读者我要写书评

暂无评论

Upper Bounds for the approximation of Some Classes of Bivariate functions by Triangular Fourier-Hermite Sums in the Space L2,ρ(Double-struck capital R²)

引用

ANALYSIS MATHEMATICA 2019年第4期45卷 823-840页

作者： Shabozov, M. Sh. Dzhurakhonov, O. A. Tajik Natl Univ Rudaki Ave 17 Dushanbe 734025 Tajikistan

We evaluate the suprema of approximations of bivariate functions by triangular partial sums of the double Fourier-Hermite series on the class of functions L (R)(2)(D) in the space L-2,L-rho(Double-struck capital R-2), where D is the second-order Hermite operator. Sharp Jackson-Stechkin type inequalities on the sets L-2,L-rho(Double-struck capital R-2) are obtained, in which the best approximation is estimated from above both in terms of moduli of continuity of order m and in terms of K-functionals. N-widths of some classes of functions in L-2,L-rho(Double-struck capital R-2) are evaluated.

关键词： upper bound approximation of functions s triangular Fourier-Hermite sum Jackson-Stechkin type inequality K-functional N-width

来源：评论

学校读者我要写书评

暂无评论

Generalized Taylor's formula for power fractional derivatives

引用

BOLETIN DE LA SOCIEDAD MATEMATICA MEXICANA 2023年第3期29卷 1-14页

作者： Zitane, Hanaa Torres, Delfim F. M. Univ Aveiro Ctr Res & Dev Math & Applicat CIDMA Dept Math P-3810193 Aveiro Portugal Univ Cape Verde Uni CV Fac Sci & Technol FCT Res Ctr Exact Sci CICE Praia 7943010 Cape Verde

We establish a new generalized Taylor's formula for power fractional derivatives with nonsingular and nonlocal kernels, which includes many known Taylor's formulas in the literature. Moreover, as a consequence, we obtain a general version of the classical mean value theorem. We apply our main result to approximate functions in Taylor's expansions at a given point. The explicit interpolation error is also obtained. The new results are illustrated through examples and numerical simulations.

关键词： approximation of functions Mean value theorem Power fractional operators Taylor's formula

来源：评论

学校读者我要写书评

暂无评论

A generalized and unified approach to the approximation of fuzzy numbers and its arithmetic and characteristics

引用

FUZZY SETS AND SYSTEMS 2023年 473卷

作者： Berenguer, M. I. Gamez, D. Garralda-Guillem, A. I. Galan, M. Ruiz Univ Granada ETS Ingn Edificac Dept Appl Math Granada Spain Univ Granada Inst Math IMAG ETS Ingn Edificac Granada Spain

In this paper we propose a general method for the approximation of an arbitrary fuzzy number. This method, which is constructive, recovers and properly extends some well-known approximations such as those obtained in terms of polygonal fuzzy numbers or simple fuzzy numbers. We prove the convergence of the general method and study the properties of the approximation operator, such as its compatibility with arithmetic operations of fuzzy numbers and with some of their important characteristics. In addition to this, we illustrate the method with some particularly interesting cases by providing algorithms, of great simplicity for practical use and apply them to some numerical examples. Furthermore, the approximations we construct are particularly simple from the point of view of fuzzy arithmetic and preserve some of their most important characteristics.

关键词： Fuzzy numbers Schauder bases approximation of functions

来源：评论

学校读者我要写书评

暂无评论

A stochastic conjugate gradient method for the approximation of functions

引用

JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS 2012年第9期236卷 2529-2544页

作者： Jiang, Hong Wilford, Paul Alcatel Lucent Bell Labs Murray Hill NJ 07974 USA

A stochastic conjugate gradient method for the approximation of a function is proposed. The proposed method avoids computing and storing the covariance matrix in the normal equations for the least squares solution. In addition, the method performs the conjugate gradient steps by using an inner product that is based on stochastic sampling. Theoretical analysis shows that the method is convergent in probability. The method has applications in such fields as predistortion for the linearization of power amplifiers. (C) 2011 Elsevier B.V. All rights reserved.

关键词： Stochastic conjugate gradient approximation of functions Convergence in probability Least squares solution Polynomial predistortion Power amplifier linearization

来源：评论

学校读者我要写书评

暂无评论

approximation of functions of Few Variables in High Dimensions

引用

CONSTRUCTIVE approximation 2011年第1期33卷 125-143页

作者： DeVore, Ronald Petrova, Guergana Wojtaszczyk, Przemyslaw Texas A&M Univ Dept Math College Stn TX 77843 USA Univ Warsaw Inst Appl Math Warsaw Poland

Let f be a continuous function defined on Omega:=[0,1] (N) which depends on only a"" coordinate variables, . We assume that we are given m and are allowed to ask for the values of f at m points in Omega. If g is in Lip1 and the coordinates i (1),aEuro broken vertical bar,i (a"") are known to us, then by asking for the values of f at m=L (a"") uniformly spaced points, we could recover f to the accuracy |g|(Lip1) L (-1) in the norm of C(Omega). This paper studies whether we can obtain similar results when the coordinates i (1),aEuro broken vertical bar,i (a"") are not known to us. A prototypical result of this paper is that by asking for C(a"")L (a"") (log (2) N) adaptively chosen point values of f, we can recover f in the uniform norm to accuracy |g|(Lip1) L (-1) when gaLip1. Similar results are proven for more general smoothness conditions on g. Results are also proven under the assumption that f can be approximated to some tolerance epsilon (which is not known) by functions of a"" variables.

关键词： approximation of functions High dimension Significant variables Sensitivity analysis

来源：评论

学校读者我要写书评

暂无评论

Complexity of approximation of functions of few variables in high dimensions

引用

JOURNAL OF COMPLEXITY 2011年第2期27卷 141-150页

作者： Wojtaszczyk, P. Univ Warsaw Inst Appl Math PL-02097 Warsaw Poland Polish Acad Sci Inst Math PL-00956 Warsaw Poland

In DeVore et al. (2011) 171 we considered smooth functions [0, 1](N) which depend on a much smaller number of variables l or continuous functions which can be approximated by such functions. We were interested in approximating those functions when we can calculate point values at points of our choice. The number of points we needed for non-adaptive algorithms was higher than that in the adaptive case. In this paper we improve on DeVore et al. (2011)[7] and show that in the non-adaptive case one can use the same number of points (up to a multiplicative constant depending on l) that we need in the adaptive case. (C) 2011 Elsevier Inc. All rights reserved.

关键词： approximation of functions High dimension Significant variables Sensitivity analysis

来源：评论

学校读者我要写书评

暂无评论

On the utility of the homotopy analysis method for non-analytic and global solutions to nonlinear differential equations

引用

NUMERICAL ALGORITHMS 2017年第1期76卷 151-162页

作者： Van Gorder, Robert A. Univ Oxford Math Inst Radcliffe Observ Quarter Andrew Wiles BldgWoodstock Rd Oxford OX2 6GG England

In recent work on the area of approximation methods for the solution of nonlinear differential equations, it has been suggested that the so-called generalized Taylor series approach is equivalent to the homotopy analysis method (HAM). In the present paper, we demonstrate that such a view is only valid in very special cases, and in general, the HAM is far more robust. In particular, the equivalence is only valid when the solution is represented as a power series in the independent variable. As has been shown many times, alternative basis functions can greatly improve the error properties of homotopy solutions, and when the base functions are not polynomials or power functions, we no longer have that the generalized Taylor series approach is equivalent to the HAM. In particular, the HAM can be used to obtain solutions which are global (defined on the whole domain) rather than local (defined on some restriction of the domain). The HAM can also be used to obtain non-analytic solutions, which by their nature can not be expressed through the generalized Taylor series approach. We demonstrate these properties of the HAM by consideration of an example where the generalizes Taylor series must always have a finite radius of convergence (and hence limited applicability), while the homotopy solution is valid over the entire infinite domain. We then give a second example for which the exact solution is not analytic, and hence, it will not agree with the generalized Taylor series over the domain. Doing so, we show that the generalized Taylor series approach is not as robust as the HAM, and hence, the HAM is more general. Such results have important implications for how iterative solutions are calculated when approximating solutions to nonlinear differential equations.

关键词： Generalized Taylor series Homotopy analysis method Nonlinear differential equations approximation of functions Analytical-numerical solution

来源：评论

学校读者我要写书评

暂无评论

Inventory management for new products with triangularly distributed demand and lead-time

引用

COMPUTERS & OPERATIONS RESEARCH 2016年 69卷 97-108页

作者： Wanke, Peter Ewbank, Henrique Leiva, Victor Rojas, Fernando Univ Fed Rio de Janeiro COPPEAD Grad Sch Business BR-21941 Rio De Janeiro Brazil Univ Adolfo Ibanez Fac Sci & Engn Santiago Chile Univ Valparaiso Sch Nutr & Dietet Valparaiso Chile

This paper proposes a computational methodology to deal with the inventory management of new products by using the triangular distribution for both demand per unit time and lead-time. The distribution for demand during lead-time (or lead-time demand) corresponds to the sum of demands per unit time, which is difficult to obtain. We consider the triangular distribution because it is useful when a distribution is unknown due to data unavailability or problems to collect them. We provide an approach to estimate the probability density function of the unknown lead-time demand distribution and use it to establish the suitable inventory model for new products by optimizing the associated costs. We evaluate the performance of the proposed methodology with simulated and real-world demand data. This methodology may be a decision support tool for managers dealing with the measurement of demand uncertainty in new products. (C) 2015 Elsevier Ltd. All rights reserved.

关键词： approximation of functions Bisection method Kernel method Kullback-Leibler divergence Monte Carlo method (Q, r) model R software Statistical distributions

来源：评论

学校读者我要写书评

暂无评论

Effective with Respect to Accuracy Algorithms of approximation of Some Classes functions by Fourier Series

引用

JOURNAL OF AUTOMATION AND INFORMATION SCIENCES 2013年第7期45卷 14-29页

作者： Zadiraka, V. K. Kolomys, E. N. Luts, L. V. Ljudvichenko, V. A. Melnikova, S. S. Natl Acad Sci Ukraine Kiev Ukraine Natl Acad Sci Ukraine VM Glushkov Cybernet Inst Kiev Ukraine Presidential Univ Interreg Acad Management & Law Inst Int Econ & Informat Technol Kiev Ukraine

The effective with respect to the accuracy algorithms of approximation of some classes functions by Fourier series are built and estimates of their errors are obtained. The proposed algorithms use, for computing the Fourier coefficients, the quadrature formulas of computing integrals of rapidly oscillating functions, optimal with respect to the accuracy and close to them.

关键词： approximation of functions Fourier series errors estimates quadrature formulas of computing integrals rapidly oscillating functions optimality with respect to the accuracy

来源：评论

学校读者我要写书评

暂无评论

建议与咨询留下您的常用邮箱和电话号码，以便我们向您反馈解决方案和替代方法

时间限定

文献类型

馆藏选择

核心期刊

语言

文献类型

帮助

文字说明：

检索规则说明：

检索范例：

分类表

所选分类

限定检索结果

文献类型

馆藏范围

日期分布

学科分类号

主题

机构

作者

语言

请选择保存的检索档案：

请选择收藏分类：

通借通还

建议与咨询 留下您的常用邮箱和电话号码，以便我们向您反馈解决方案和替代方法

时间限定

文献类型

馆藏选择

核心期刊

语言

文献类型

帮助

文字说明：

检索规则说明：

检索范例：

分类表

所选分类

限定检索结果

文献类型

馆藏范围

日期分布

学科分类号

主题

机构

作者

语言

请选择保存的检索档案： 新增检索档案 确定 取消

请选择收藏分类： 新增自定义分类 确定 取消

通借通还

建议与咨询留下您的常用邮箱和电话号码，以便我们向您反馈解决方案和替代方法

请选择保存的检索档案：

请选择收藏分类：