导弹武器系统费用预测的径向基函数网络方法

提出采用径向基函数网络理论来估算导弹武器系统的费用,武器系统的费用与武器特征参数的关系可通过神经网络的阈值和权值来表现,并且对几种用于导弹武器系统费用分析的数据分析结果进行比较分析.通过实例说明了应用径向基函数网络进行导弹武器系统费用分析不但算法可行性好、拟合精度高,而且具有运算简单,结果可靠的特点.     

基于Gauss全局径向基函数的近岸浅水变形波高数值计算新方法

应用Gauss全局径向基函数来模拟波浪浅水变形波高变化方程中的未知函数,经实例分析探讨得到了一种可用于求解该方程数值解的新方法,并将其计算结果与常用数值分析方法得到的数值解相互对比印证,证明了基于Gauss全局径向基函数法计算结果的正确性.经验证,Gauss径向基函数法的平均计算误差相比其他方法均要小,表明该方法拥有更高的计算精度.同时,根据Gauss全局径向基函数的逼近结果,得出了浅水变形波高变化微分方程数值解的拟合函数,在实际工程中,可以利用该拟合函数来代替原方程的解析解,研究成果可为求解近岸浅水区域波浪运动提供一种新思路.     

神经网络的函数逼近能力分析

本文综述了多层前传网络（ＭＬＰ）及径向基函数网络（ＲＢＦ）对函数任意精度逼近的能力，比较了两种网络的最佳逼近特性。对激活函数类的扩充作了介绍，并说明有限数值精度对函数逼近能力实现的影响。     

基于径向基函数网络的虚拟物流企业伙伴选择方法研究

在对虚拟物流企业系统研究的基础上 ,针对虚拟物流企业伙伴选择问题的特点 ,给出了一个面对虚拟物流企业伙伴选择问题的较为全面的选择过程框架 .并提出了一个基于径向基函数网络算法的虚拟物流企业伙伴选择模型 ,实例仿真说明了该算法和模型的有效性 .     

球面混合插值的逼近性质

球面径向基函数(SBF)和多项式样条函数均为处理球面散乱数据的有效工具. 本文考虑由球面径向基函数与球面多项式函数组成的混合插值模型, 并利用最小二乘法求解该模型. 对于该插值模型, 首先, 给出带Bessel势的Sobolev空间中的Bernstein不等式, 然后利用该不等式建立逼近正定理,并进一步给出该插值工具的误差估计. 最后, 研究该插值方式(即利用最小二乘法求解混合插值模型)的稳定性.     

聚类优化RBF网络在锅炉燃烧中的应用

为了提高径向神经网络的训练精度,提出一种混合优化算法.算法将基于萤火虫算法的模糊聚类,应用到径向神经网络基函数中心向量的计算中,利用萤火虫算法良好的全局寻优能力来优化搜索基函数中心,提高了获取网络类中心的稳定性.锅炉燃烧优化的实例表明,混合优化算法达到了预期效果,提升了锅炉燃烧效率.     

球面上径向基函数最小范数插值逼近的误差估计

研究了球面径向基插值对球面函数的逼近问题,给出了一致逼近的上界估计式．文中结果说明,球面径向基插值的逼近阶会随函数光滑性的提高而增加．     

Switching Control of Nonlinear Systems Based on the Quasi-ARX Model and the SVR Algorithm北大核心CSCD

该文基于改进的含有外部输入项的准线性自回归(准ARX)径向基函数(RBF)网络模型和支持向量回归(SVR)算法,提出了一种非线性切换控制方法.改进的准ARX模型非线性部分采用RBF网络.控制系统设计过程分为三个部分:首先,利用聚类方法确定模型的非线性参数;然后,采用线性SVR算法来解决控制系统的鲁棒性问题;接下来,基于控制误差给出切换判定函数,确定切换律给出控制序列.最后通过数值仿真验证了该方法的有效性.     

求解扩散方程的非对称径向基函数配点法

本文针对扩散方程,借助于Halton节点,基于径向基函数和迭代法提出一种新的无网格方法.该方法在时间层上采用全隐离散,在空间层上构造了θ-型迭代格式,然后利用径向基函数去逼近未知函数.由于本文采用紧支集径向基函数,因而导出的离散系统矩阵是稀疏的,且有较好的条件数.最后通过数值实验验证新方法的有效性.     

基于FOA-RBF神经网络的外贸出口预测

应用果蝇优化算法对径向基神经网络扩展参数的优化方法进行研究,给出了一种以标准误差计算公式为味道判定函数,以此确定最优的径向基函数的扩展参数值的方法,并建立了相应的预测模型.应用该预测模型对黑龙江省外贸出口额进行预测,结果表明:预测模型的预测精度优于径向基神经网络,从而证明了方法的有效性.     

On similarities between two models of global optimization: statistical models and radial basis functions

Construction of global optimization algorithms using statistical models and radial basis function models is discussed. A new method of data smoothing using radial basis function and least squares approach is presented. It is shown that the P-algorithm for global optimization in the presence of noise based on a statistical model coincides with the corresponding radial basis algorithm.     

Approximation in rough native spaces by shifts of smooth kernels on spheres

Within the conventional framework of a native space structure, a smooth kernel generates a small native space, and “radial basis functions” stemming from the smooth kernel are intended to approximate only functions from this small native space. Therefore their approximation power is quite limited. Recently, Narcowich et al. (J. Approx. Theory 114 (2002) 70), and Narcowich and Ward (SIAM J. Math. Anal., to appear), respectively, have studied two approaches that have led to the empowerment of smooth radial basis functions in a larger native space. In the approach of [NW], the radial basis function interpolates the target function at some scattered (prescribed) points. In both approaches, approximation power of the smooth radial basis functions is achieved by utilizing spherical polynomials of a (possibly) large degree to form an intermediate approximation between the radial basis approximation and the target function. In this paper, we take a new approach. We embed the smooth radial basis functions in a larger native space generated by a less smooth kernel, and use them to approximate functions from the larger native space. Among other results, we characterize the best approximant with respect to the metric of the larger native space to be the radial basis function that interpolates the target function on a set of finite scattered points after the action of a certain multiplier operator. We also establish the error bounds between the best approximant and the target function.     

Radial Multiresolution in Dimension Three

We present a construction of a wavelet-type orthonormal basis for the space of radial $L^2$-functions in {\bf R}$^3$ via the concept of a radial multiresolution analysis. The elements of the basis are obtained from a single radial wavelet by usual dilations and generalized translations. Hereby the generalized translation reveals the group convolution of radial functions in {\bf R}$^3$. We provide a simple way to construct a radial scaling function and a radial wavelet from an even classical scaling function on {\bf R}. Furthermore, decomposition and reconstruction algorithms are formulated.     

函数的径向基表示

本文是关于函数的径向表示的综述性文章，基于我们对这方面的研究工作的了解，介绍了国际上近年来这方面的主要的有关研究结果以及在一些领域中应用的情况，文后附有主要的参考文献以便感兴趣的读者查阅。     

Comparison of Radial Basis Functions

A survey of algorithms for approximation of multivariate functions with radial basis function (RBF) splines is presented. Algorithms of interpolating, smoothing, selecting the smoothing parameter, and regression with splines are described in detail. These algorithms are based on the feature of conditional positive definiteness of the spline radial basis function. Several families of radial basis functions generated by means of conditionally completely monotone functions are considered. Recommendations for the selection of the spline basis and preparation of initial data for approximation with the help of the RBF spline are given.     

用径向基函数插值解自共轭椭圆型方程

本文讨论用MQ作为插值的径向基函数,对自共轭椭圆型方程进行插值,证明了插值系数的唯一性,并用投影法证明了用径向基函数解自共轭椭圆型方程的收敛性.     

A Quasi-Interpolation Satisfying Quadratic Polynomial Reproduction with Radial Basis Functions

In this paper,a new quasi-interpolation with radial basis functions which satis- fies quadratic polynomial reproduction is constructed on the infinite set of equally spaced data.A new basis function is constructed by making convolution integral with a constructed spline and a given radial basis function.In particular,for twicely differ- entiable function the proposed method provides better approximation and also takes care of derivatives approximation.     

Construction of adapted subdivision schemes for bounded intervals based on radial basis function interpolation

We study stationary subdivision schemes based on radial basis function interpolation. Each scheme has a tension parameter, say λ, which actually belongs to the radial basis function. In particular, adapted subdivision rules on bounded intervals are developed.     

Radial basis function partition of unity operator splitting method for pricing multi-asset American options

The operator splitting method in combination with finite differences has been shown to be an efficient approach for pricing American options numerically. Here, the operator splitting formulation is extended to the radial basis function partition of unity method. An approach that has previously often been used together with radial basis function methods to deal with the free boundary arising in American option pricing is to solve a penalised version of the Black–Scholes equation. It is shown that the operator splitting technique outperforms the penalty approach when used with the radial basis function partition of unity method. Numerical experiments are performed for one, two and three underlying assets. The advantage of the operator splitting technique grows with the number of dimensions.     

Iterative adaptive RBF methods for detection of edges in two-dimensional functions

Radial basis functions have gained popularity for many applications including numerical solution of partial differential equations, image processing, and machine learning. For these applications it is useful to have an algorithm which detects edges or sharp gradients and is based on the underlying basis functions. In our previous research, we proposed an iterative adaptive multiquadric radial basis function method for the detection of local jump discontinuities in one-dimensional problems. The iterative edge detection method is based on the observation that the absolute values of the expansion coefficients of multiquadric radial basis function approximation grow exponentially in the presence of a local jump discontinuity with fixed shape parameters but grow only linearly with vanishing shape parameters. The different growth rate allows us to accurately detect edges in the radial basis function approximation. In this work, we extend the one-dimensional iterative edge detection method to two-dimensional problems. We consider two approaches: the dimension-by-dimension technique and the global extension approach. In both cases, we use a rescaling method to avoid ill-conditioning of the interpolation matrix. The global extension approach is less efficient than the dimension-by-dimension approach, but is applicable to truly scattered two-dimensional points, whereas the dimension-by-dimension approach requires tensor product grids. Numerical examples using both approaches demonstrate that the two-dimensional iterative adaptive radial basis function method yields accurate results.