共查询到20条相似文献,搜索用时 546 毫秒
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将光滑的球面基函数φ嵌入到由一个不充分光滑的球面基函数ψ生成的本性空间Nψ中,并在Lp度量下研究由φ的变换生成的函数在空间Nψ中的逼近性质,得到了该Lp逼近的误差估计. 相似文献
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《数学年刊A辑(中文版)》2010,(5)
将光滑的球面基函数φ嵌入到由一个不充分光滑的球面基函数Ψ生成的本性空间N_Ψ中,并在L~p度量下研究由φ的变换生成的函数在空间N_Ψ中的逼近性质,得到了该L~p逼近的误差估计. 相似文献
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研究了径向基网络插值算法与3D曲面重构方法,分别从研究价值、插值理论、仿真等等方面做了详细分析,研究结果表明RBF-Network在逼近一维复杂的非线性函数时具有收敛速度快、精度高、泛化能力更强等优点.但在3D重构方面,基于RBF的单位分解法重构效果更好. 相似文献
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研究了球型平移网络对周期函数的逼近问题.文章首先将基函数eimx分别表示成为两种球型平移网络.进一步,将有关多重Fourier级数的Bochner-Riesz平均表示成为球型平移网络的形式.在此基础上构造出了两类球型平移网络序列,并借助于有关Bochner-Riesz平均对Lp空间中函数的逼近结果给出了这两类球型平移网络序列在Lp空间中的逼近阶. 相似文献
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球面带形平移网络逼近的Jackson定理 总被引:2,自引:0,他引:2
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. 相似文献
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Mohammadreza Ahmadi
Darani Davoud Mirzaei 《Numerical Methods for Partial Differential Equations》2020,36(6):1682-1698
This paper concerns a numerical solution for the diffusion equation on the unit sphere. The given method is based on the spherical basis function approximation and the Petrov–Galerkin test discretization. The method is meshless because spherical triangulation is not required neither for approximation nor for numerical integration. This feature is achieved through the spherical basis function approximation and the use of local weak forms instead of a global variational formulation. The local Petrov–Galerkin formulation allows to compute the integrals on small independent spherical caps without any dependence on a connected background mesh. Experimental results show the accuracy and the efficiency of the new method. 相似文献
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Error estimates for scattered data interpolation on spheres 总被引:5,自引:0,他引:5
We study Sobolev type estimates for the approximation order resulting from using strictly positive definite kernels to do interpolation on the -sphere. The interpolation knots are scattered. Our approach partly follows the general theory of Golomb and Weinberger and related estimates. These error estimates are then based on series expansions of smooth functions in terms of spherical harmonics. The Markov inequality for spherical harmonics is essential to our analysis and is used in order to find lower bounds for certain sampling operators on spaces of spherical harmonics.
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Zhixiang Chen Feilong Cao Ming Li 《Mathematical Methods in the Applied Sciences》2015,38(12):2527-2536
This paper studies the construction and approximation of quasi‐interpolation for spherical scattered data. First of all, a kind of quasi‐interpolation operator with Gaussian kernel is constructed to approximate the spherical function, and two Jackson type theorems are established. Second, the classical Shepard operator is extended from Euclidean space to the unit sphere, and the error of approximation by the spherical Shepard operator is estimated. Finally, the compact supported kernel is used to construct quasi‐interpolation operator for fitting spherical scattered data, where the spherical modulus of continuity and separation distance of scattered sampling points are employed as the measurements of approximation error. Copyright © 2014 John Wiley & Sons, Ltd. 相似文献
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On the Degree of Approximation by Spherical Translations 总被引:1,自引:0,他引:1
Bao-huai Sheng 《应用数学学报(英文版)》2006,22(4):671-680
The degree of approximation of spherical functions by the translations formed by a function defined on the unit sphere is dealt with. A kind of Jackson inequality is established under the condition that none of the L^2(S^q) norms of the orthogonal projection operators of the translated function are zeros. In the present paper we show that the spherical translations share the same degree of approximation as that of spherical harmonics. 相似文献
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Feilong Cao Huazhong Wang Shaobo Lin 《Mathematical Methods in the Applied Sciences》2011,34(15):1888-1895
Compared with planar hyperplane, fitting data on the sphere has been an important and an active issue in geoscience, metrology, brain imaging, and so on. In this paper, with the help of the Jackson‐type theorem of polynomial approximation on the sphere, we construct spherical feed‐forward neural networks to approximate the continuous function defined on the sphere. As a metric, the modulus of smoothness of spherical function is used to measure the error of the approximation, and a Jackson‐type theorem on the approximation is established. Copyright © 2011 John Wiley & Sons, Ltd. 相似文献
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We consider the linearized scalar potential formulation of the magnetostatic field problem in this paper. Our approach involves a reformulation of the continuous problem as a parametric boundary problem. By the introduction of a spherical interface and the use of spherical harmonics, the infinite boundary conditions can also be satisfied in the parametric framework. That is the field in the exterior of a sphere is expanded in a ‘harmonic series’ of eigenfunctions for the exterior harmonic problem. The approach is essentially a finite element method coupled with a spectral method via a boundary parametric procedure. The reformulated problem is discretized by finite element techniques which leads to a discrete parametric problem which can be solved by well conditioned iteration involving only the solution of decoupled Neumann type elliptic finite element systems and L2 projection onto subspaces of spherical harmonics. Error and stability estimates given show exponential convergence in the degree of the spherical harmonics and optimal order convergence with respect to the finite element approximation for the resulting fields in L2. 相似文献
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Zhixiang Chen 《分析论及其应用》2007,23(4):325-333
The spherical approximation between two nested reproducing kernels Hilbert spaces generated from different smooth kernels is investigated. It is shown that the functions of a space can be approximated by that of the subspace with better smoothness. Furthermore, the upper bound of approximation error is given. 相似文献