共查询到20条相似文献,搜索用时 421 毫秒
1.
Leonardo Colzani Leonede De Michele Delfina Roux 《Mediterranean Journal of Mathematics》2012,9(2):253-266
Although Fourier series or integrals of piecewise smooth functions may be slowly convergent, sometimes it is possible to accelerate their speed of convergence by adding and subtracting suitable combination of known functions. 相似文献
2.
W. L. Hare 《Computational Optimization and Applications》2006,33(2-3):249-270
The past decade has seen the introduction of a number of classes of nonsmooth functions possessing smooth substructure, e.g., “amenable functions”, “partly smooth functions”, and “g ° F decomposable functions”. Along with these classes a number of structural properties have been proposed, e.g., “identifiable surfaces”, “fast tracks”, and “primal-dual gradient structures”. In this paper we examine the relationships between these various classes of functions and their smooth substructures. In the convex case we show that the definitions of identifiable surfaces, fast tracks, and partly smooth functions are equivalent. In the nonconvex case we discuss when a primal-dual gradient structure or g ° F decomposition implies the function is partly smooth, and vice versa. We further provide examples to show these classes are not equal. 相似文献
3.
A Property of Piecewise Smooth Functions 总被引:1,自引:0,他引:1
R.T. Rockafellar 《Computational Optimization and Applications》2003,25(1-3):247-250
Piecewise smooth equations are increasingly important in the numerical treatment of complementarity problems and models of equilibrium. This note brings out a property of the functions that enter such equations, for instance through penalty expressions. 相似文献
4.
We obtain conditions under which the Morse functions defined on surfaces are smooth equivalent and functions with isolated critical (singular) points are topologically equivalent. 相似文献
5.
光滑函数集列紧的一个判据 总被引:1,自引:1,他引:0
张伟年 《数学的实践与认识》1997,(4)
本文讨论紧区间上的C~1光滑函数,用6-网构造法证明了这种函数集合列紧的一个判据,从而使著名的Ascoli-Arzela引理在光滑情形下得到推广,这一结果对讨论光滑动力系统有重要意义。 相似文献
6.
Based on the previously developed technique using the Laplace transformation of distributions with compact support, we calculate the Hochschild cohomologies of the algebra of smooth functions on a finite-dimensional real vector space with coefficients in the adjoint representation. 相似文献
7.
首先证明了Frechet光滑Banach空间上齐次函数的次微分的一个有用定理,然后利用下半连续函数和的次微分规则把Clarke-Ledyaev多方向中值不等式推广到多个函数的情形. 相似文献
8.
9.
Ricardo Estrada 《Proceedings of the American Mathematical Society》1998,126(3):761-768
The existence of rapidly decreasing smooth solutions of moment problems for functions of several variables with values in a Fréchet space is obtained. It is shown that the corresponding results for functions with values in a general topological vector space do not hold.
10.
V. V. Zhikov 《Journal of Mathematical Sciences》2006,132(3):285-294
We study the problem on density of smooth functions in Sobolev spaces of variable orders, also called Sobolev-Orlicz spaces.
In particular, we generalize the earlier obtained logarithmic condition and give a number of examples. Bibliography: 9 titles.
__________
Translated from Zapiski Nauchnykh Seminarov POMI, Vol. 310, 2004, pp. 67–81. 相似文献
11.
Michael Langenbruch 《Results in Mathematics》1999,36(3-4):281-296
Let F be a closed proper subset of ?n and let ?* be a class of ultradifferentiable functions. We give a new proof for the following result of Schmets and Valdivia on analytic modification of smooth functions: for every function ? ∈ ?* (?n) there is ${\widetilde f} \in {\cal E}_{*}(\rm R ^{n})$ which is real analytic on ?nF and such that ?a ? ¦ F = ?a ? ¦ F for any a ∈ ?0 n. For bounded ultradifferentiable functions ? we can obtain ${\widetilde f}$ by means of a continuous linear operator. 相似文献
12.
James M. Calvin Antanas Žilinskas 《Journal of Optimization Theory and Applications》2014,163(2):528-547
The problem of approximating the global minimum of a function of two variables is considered. A method is proposed rooted in the statistical approach to global optimization. The proposed algorithm partitions the feasible region using a Delaunay triangulation. Only the objective function values are required by the optimization algorithm. The asymptotic convergence rate is analyzed for a class of smooth functions. Numerical examples are provided. 相似文献
13.
首先,引入一种由斜坡函数激发的神经网络算子,建立了其对连续函数逼近的正、逆定理,给出了其本质逼近阶.其次,引入这种神经网络算子的线性组合以提高逼近阶,并且研究了这种组合的同时逼近问题.最后,利用Steklov函数构造了一种新的神经网络算子,建立了其在L~p[a,b]空间逼近的正、逆定理. 相似文献
14.
For Fourier expansions of piecewise smooth functions associated with an elliptic
operator of order m in Rn, the sets of uniform convergence are described. 相似文献
15.
V. V. Zharinov 《Theoretical and Mathematical Physics》2005,144(3):1247-1263
We calculate the Hochschild cohomology of the algebra of smooth functions on a finite-dimensional real torus with coefficients in the adjoint representation, generalizing the previously developed technique to the discrete case for this.__________Translated from Teoreticheskaya i Matematicheskaya Fizika, Vol. 144, No. 3, pp. 435–452, September, 2005. 相似文献
16.
Approximation of Smooth Functions and Constants by Polynomials with Integer and Natural Coefficients
Direct theorems on the approximation of smooth functions by polynomials with integer coefficients are strengthened. First theorems on approximation by polynomials with natural coefficients are obtained. 相似文献
17.
A Peak Point Theorem for Uniform Algebras Generated by Smooth Functions on Two-Manifolds 总被引:1,自引:0,他引:1
We establish the peak point conjecture for uniform algebrasgenerated by smooth functions on two-manifolds: if A is a uniformalgebra generated by smooth functions on a compact smooth two-manifoldM, such that the maximal ideal space of A is M, and every pointof M is a peak point for A, then A = C(M). We also give an alternativeproof in the case when the algebra A is the uniform closureP(M) of the polynomials on a polynomially convex smooth two-manifoldM lying in a strictly pseudoconvex hypersurface in Cn. 相似文献
18.
Mathematical Notes - The closure of the set of smooth compactly supported functions in a weighted Hölder space on ?n, n ≥ 1, with a weight controlling the behavior at the point at... 相似文献
19.
PowerNet: Efficient Representations of Polynomials and Smooth Functions by Deep Neural Networks with Rectified Power Units 下载免费PDF全文
Deep neural network with rectified linear units (ReLU) is getting more and
more popular recently. However, the derivatives of the function represented by a ReLU
network are not continuous, which limit the usage of ReLU network to situations only
when smoothness is not required. In this paper, we construct deep neural networks
with rectified power units (RePU), which can give better approximations for smooth
functions. Optimal algorithms are proposed to explicitly build neural networks with
sparsely connected RePUs, which we call PowerNets, to represent polynomials with
no approximation error. For general smooth functions, we first project the function to
their polynomial approximations, then use the proposed algorithms to construct corresponding PowerNets. Thus, the error of best polynomial approximation provides an
upper bound of the best RePU network approximation error. For smooth functions in
higher dimensional Sobolev spaces, we use fast spectral transforms for tensor-product
grid and sparse grid discretization to get polynomial approximations. Our constructive algorithms show clearly a close connection between spectral methods and deep
neural networks: PowerNets with $n$ hidden layers can exactly represent polynomials
up to degree $s^n$, where $s$ is the power of RePUs. The proposed PowerNets have potential applications in the situations where high-accuracy is desired or smoothness is
required. 相似文献
20.
1.IntroductionConsidersmoothcompositionsofmax-typefunctionsoftheform:f(x)=g(x,aestfij(x),'',,T?:fmj(x)),(1.1)wherexER",Ji,i~1,'',marefiniteindexsets,gandfij,jEJi,i=1,'',marecontinuouslydifferentiableonRill 71andR;'respectively.Thisclassofnonsmoothfunct… 相似文献