一种新的光滑支持向量机的构造及其应用

光滑支持向量机模型是一个无约束、可微的最优化模型,人们可应用快速的最优化方法求解,从而降低计算复杂性.在前人工作的基础上研究基于样条函数的光滑支持向量机,采用广义三弯矩方法构造出六次样条光滑函数,分析了其性能及与正号函数的逼近精度,实现了求解六次样条光滑支持向量机的算法,与其它光滑支持向量机进行了比较,取得了较好的结果.最后将其应用于心脏病模型诊断,实验结果显示具有较高的精确度.     

关于Varma的缺插值样条函数

最近,A.K.Varma在中讨论了五次、六次缺插值样条函数。 设n=2m 1,x_i=i/2m,i=0,2,…,2m.用S_(nō)~(2)(x)表示在[0,1]上满足下列条件的五次样条函数     

一类四次有理插值样条的点控制

构造了一种有理四次插值样条,其分子为四次多项式分母为二次多项式.该有理插值样条是有界的、保单调且C~2连续的,仅带有一个调节参数δ_i.研究了有理四次插值样条的性质,同时给出了相应的函数值控制、导数值控制方法,这种方法的优点在于能够根据实际设计需要简单地选取适宜的参数,达到对曲线的形状进行局部调控的目的.     

带形状参数控制的三次B样条曲线曲面的光顺

三次B样条曲线是一种广泛应用于计算机辅助几何设计中的非常重要的曲线.本文在以曲线的最小应变能作为衡量曲线光顺性的基础上,采用带调节控制参数的方法分别对三次B样条曲线和双三次B样条曲面进行了光顺处理.由所提供的方法以及实例可以看出,本方法可在曲线曲面光顺的基础上通过修改参数大小以达到控制曲线曲面形状的目的,且修改后的点的位置与原坏点的距离是由参数的大小控制决定的,这样就使得我们的光顺处理可以控制在数据测量的误差范围内.     

一类缺插值样条的分析方法

本文讨论一类缺插值样条的一种分析方法,它的基本思想,来自[1]中对五次样条的一些讨论. 作者运用这种方法已对一类特殊的三次样条和七次样条以及下文中要讨论的五次、11次样条进行了分析,发现这类样条都可以通过预定的、有限的步骤获得它们的一些渐近式、逼近度及饱和度的结果.从结果看,它们的这些性质是那样的相似,可以说它们是这类缺插值样条的本质特征. 本文从五次缺插值样条开始,在§1中给出它的一些新的结果.     

一类基于l1模的最佳二次样条插值

本文讨论了二次样条插值的定解条件,在l_1模意义下给出了一类最佳二次样条插值的概念,以及寻找最佳二次样条插值的定解条件的方法.最后讨论了误差估计问题,并给出了实际算例.     

奇次样条的渐近展开

渐近展开理论的研究在数值计算中有着广泛的应用,在逼近理论研究中也是一个重要的课题,然而,对于样条的渐近展开的工作,见得还不多.作者在〔1〕中讨论了几类缺插值样条函数的渐近展开,在〔2〕中讨论了五次样条的渐近展开,从上述文章中可以看出,五次样条情形已经相当繁复了,也就是说,单用 Hermite 插值方法很难导出一般n 次样条的渐近展开.本文结合 B-Spline,运用一些技巧可以得到 n 次样条的渐近展开,     

基于再生核三次样条基底的构造及其应用

将三次样条理论与再生核理论相结合,利用再生核函数巧妙地构造了三次样条函数空间的一组基底.基于三次样条插值的高收敛特点,得到了微分方程边值问题近似解的一种新的求解方法.数值算例展现出算法简单、有效.     

二元二次分片多项式插值样条函数

本文在Ⅱ型剖分下,研究一类二元二次分片多项式插值样条函数,采用局部坐标系和本文定理1的拼接技巧,揭示了二元二次样条与一元二次样条之间的紧密联系.只要在垂直网线和水平网线上先构造出一元二次样条并求出它们在节点上的一些数据,就可直接写出二元二次样条的分块解析表示式.利用这种技巧,可以进一步研究各种类型的插值样条,还可用来研究双周期或单周期的插值样条.本文证明了,这类样条函数具有与一元二次样条相同的逼近阶,具体来讲,在不均匀剖分且 f(x,y)∈σ~3[a,b;c,d]时,它的逼近阶是2,在均匀剖分且 f(x,y)∈σ~4[a,b;c,d]时,其逼近阶是3.用本文的方法去研究其他各类插值样条,发现也有这种逼近性质.     

基于三次样条插值函数的非线性动力系统数值求解

三次样条插值函数具有良好的收敛性、稳定性与二阶光滑性.研究了借助三次样条插值函数构造的非线性动力系统数值求解方法,分析了该方法与已有的非线性动力系统数值求解方法的优缺点,刻画了误差估计且给出了数值算例.结果表明基于三次样条插值函数构造的数值方法比已有的方法收敛速度快、逼近精度高且能够很好地逼近非线性动力系统的解析解.     

Qualitative Analysis of Bifurcating Solutions in the Lengyel-Epstein Model

One of the most fundamental problems in theoretical biology is to explain the mechanisms by which patterns and forms are created in the＇living world. In his seminal paper ＂The Chemical Basis of Morphogenesis＂, Turing showed that a system of coupled reaction-diffusion equations can be used to describe patterns and forms in biological systems. However, the first experimental evidence to the Turing patterns was observed by De Kepper and her associates（1990） on the CIMA reaction in an open unstirred reactor, almost 40 years after Turing＇s prediction. Lengyel and Epstein characterized this famous experiment using a system of reaction-diffusion equations. The Lengyel-Epstein model is in the form as follows     

(0,1 ;0)-INTERPOLATION ON INFINITE INTERVAL (-∞, +∞)

In this paper, we study the explicit representation and convergence of (0, 1; 0)-interpolation on infinite interval, which means to determine a polynomial of degree ≤ 3n - 2 when the function values are prescribed at two set of points namely the zeros of Hn(x) and H′n(x) and the first derivatives at the zeros of H′n(x).     

RECENT PROGRESS ON SPHERICAL HARMONIC APPROXIMATION MADE BY BNU RESEARCH GROUP ——In memory of Professor Sun Yongsheng

As early as in 1990, Professor Sun Yongsheng, suggested his students at Beijing Normal University to consider research problems on the unit sphere. Under his guidance and encouragement his students started the research on spherical harmonic analysis and approximation. In this paper, we incompletely introduce the main achievements in this area obtained by our group and relative researchers during recent 5 years （2001-2005）. The main topics are： convergence of Cesaro summability, a.e. and strong summability of Fourier-Laplace series; smoothness and K-functionals; Kolmogorov and linear widths.     

A REPRESENTATION FORMULA RELATED TO SCHR(O)DINGER OPERATORS

Schr(o)dinger operator is a central subject in the mathematical study of quantum mechanics.Consider the Schrodinger operator H = -△ V on R, where △ = d2/dx2 and the potential function V is real valued. In Fourier analysis, it is well-known that a square integrable function admits an expansion with exponentials as eigenfunctions of -△. A natural conjecture is that an L2 function admits a similar expansion in terms of "eigenfunctions" of H, a perturbation of the Laplacian (see [7], Ch. Ⅺ and the notes), under certain condition on V.     

Journal of the Operations Research Society of China Special issue on Operations Research in Healthcare Management

正Guest Editors:Hong Chen,Shanghai Jiao Tong University,Shanghai,China Guohua Wan,Shanghai Jiao Tong University,Shanghai,China David Yao,Columbia University,New York,USA Scope:Healthcare delivery worldwide has been fraught with high cost,low efficiency and poor quality of patient care service.For the field of operations research(OR),healthcare offers some of the biggest challenges as well as best opportunities in     

ANALYSIS IN THEORY AND APPLICATIONS Vol. 30, 2014 CONTENTS

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An alternative mathematical algorithm for the photo- and videokeratoscope

Due to the resolution of current laser technology, the accuracy of corneal topography as measured by the videokeratoscope is no longer adequate to provide precise enough data for refractive surgery or for the fitting of customized contact lenses. We present an algorithm for recovering corneal topography that makes use of modern differential geometric techniques and numerical descent in Sobolev spaces. We believe this algorithm may be used with the photo- and videokeratoscope to increase the accuracy of the recovered corneal topography.     

A note on Sobolev orthogonality for Laguerre matrix polynomials

Let {Ln(A,λ)(x)}n≥0 be the sequence of monic Laguerre matrix polynomials defined on [0, ∞) by Ln(A,λ)(x)=n!/(-λ)n∑nk=0(-λ)κ/k!(n-1)! (A I)n[(A I)k]-1 xk,where A ∈ Cr×r. It is known that {Ln(A,λ)(x)}n≥0 is orthogonal with respect to a matrix moment functional when A satisfies the spectral condition that Re(z) ＞ - 1 for every z ∈σ(A).In this note we show that forA such that σ(A) does not contain negative integers, the Laguerre matrix polynomials Ln(A,λ) (x) are orthogonal with respect to a non-diagonal SobolevLaguerre matrix moment functional, which extends two cases: the above matrix case and the known scalar case.     

CONTENTS OF VOLUME 30

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