二元三次样条空间S_3~(1,2)(△_(mn)~(2))的样条拟插值

本文首先利用由两组具有局部最小支集的样条所组成的基函数,构造非均匀2型三角剖分上二元三次样条空间S1,23(△(2)mn)的若干样条拟插值算子.这些变差缩减算子由样条函数B1ij支集上5个网格点或中心和样条函数B2ij支集上5个网格点处函数值定义.这些样条拟插值算子具有较好的逼近性,甚至算子Vmn(f)能保持近最优的三次多项式性.然后利用连续模,分析样条拟插值算子Vmn(f)一致逼近于充分光滑的实函数.最后推导误差估计.     

广义Ⅱ型三角剖分下二元样条函数空间S_2~1(■_(mn))的维数

<正>1引言假设Ω是平面上任一单连通的多边形区域,△是它的任一正规三角剖分,T表示△中所有三角形的集合.对满足0≤rd的非负整数d,r,定义二元d次r阶光滑样条函数空间     

S_2~1(△_(mn)~((2)))上的整节点插值

[1]中提出一种二元样条的插值方法,后来[2]对此种方法进行了较深入的分析.[2]中区分了二种不同类型的插值点:基本插值点和附加插值点;也给出了两种不同类型的插值:整节点插值和半整节点插值。本文研究空间S_2~1(△_(mn)~((2)))上的整节点插值,讨论插值     

样条空间S_3~1（△_（mn）~（1））上的插值与逼近

本文讨论样条空间Ｓ１３（△_（１）~ｍｎ）上的插值问题，导出了一类插值条件下样条插值的存在性与唯一性结论以及计算插值样条的递推格式．其主要结论是对四阶光滑的函数，插值排条可达２阶（相对网格长度）逼近度．     

关于插值样条S_k~1(⊿_(mn)~((i)))

本文对 S_k~1(Δ_(mn)~(i))(i=1,2)插值问题给出一个一般性的研究方法,并以 S_4~1(Δ_(mn)~(1))为例,作了具体的应用,于是它的一类插值样条的存在、唯一性以及逼近度得以顺利解决.     

关于S_3~1(Δ_(mn)~((1)))插值问题(Ⅰ)

设Δ_(mn)~(1)是长方形区域D=[0,mh_1]×[0,nh_2]上的如图1所示的剖分:为本文方便起见,设h_1=h_2=h,事 实上h_1 h_2时,本文的方法完全适用。 则Δ_(mn)~(1):x=ih,y=jh,x-y=     

Morgan-Scott剖分上样条空间S_8~4(Δ_(ms))的维数

Ｍｏｒｇｅｎ－Ｓｃｏｔ剖分上样条空间的维数依赖于剖分的几何性质，本文证明了Ｄｉｅｎｅｒ１９９０年提出的猜想对ｒ＝４是不正确的，需要修正．     

关于插值样条S_k~l(⊿_(mn)~((i)))

本文对(i=1,2)插值问题给出一个一般性的研究方法,并以为例,作了具体的应用,于是它的一类插值样条的存在、唯一性以及逼近度得以顺利解决。     

关于S_2~1(Δ_(mn)~((2)))的一个恒等式

本文将得到关于S_2~1(Δ_(mn)~(2))的一个恒等式,它对某些带限制的S_2~1(Δ_(mn)~(2))问题,提供了一个方便工具。 矩形域D_i[0,l_1]×[0,l_2],它的Δ_(mn)~(2)剖分是熟知的(见下图所示),在图上标了某些记号,这是讨论中需要的。记h_1=l_1/m,h_2=l_2/n,且节点(ih_1,jh_2)将简记为(i,j)。     

QUASI-INTERPOLATING OPERATORS AND THEIR APPLICATIONS IN HYPERSINGULAR INTEGRALS

1.IntroductionSinceP.ZwartobtainedanexpressionofbivariateB--spline[2],R.--HWangandC.K.Chuihavedevelopedaseriesofresults,especially,thequasi--interpolatingoperatorsofSI(AL.)onuniformtype-2triangulationanditsapproximationproperties[']whichhavewidespreadapplicationsinMechanicsandEngineering.Furthermore,R-HWangandC.K.ChuialsoobtainedthefunctionwithminimumsupportinSI(A:)onnon-uniformtype-2triangulationandthebasisofSI(a:)[#].Inthispaperweintroducesomequasi-interpolatingoperatorsofSa(~Z~)o…     

计算二维Cauchy主值积分的多元样条方法

本文采用非均匀２－型三角剖分上的样条函数空间Ｓ２＾１（Δｍｎ＾２）中的拟插值方法，构造了一类计算二维Ｃａｕｃｈｙ主值积分的数值求积公式，并对其逼近误差进行了研究。同时通过算例验证了此方法的有效性。     

Bivariate quartic spline spaces and quasi-interpolation operators

In this paper, we study two bivariate quartic spline spaces and , and present two classes of quasi-interpolation operators in the two spaces, respectively. Some results on the operators are given.     

The Bases of the Non-Uniform Cubic Spline Space $S_{3}^{1,2}(\Delta_{mn}^{(2)})$

In this paper, the dimension of the nonuniform bivariate spline space $S_{3}^{1,2}(\Delta_{mn}^{(2)})$ is discussed based on the theory of multivariate spline space. Moreover, by means of the Conformality of Smoothing Cofactor Method, the basis of $S_{3}^{1,2}(\Delta_{mn}^{(2)}) $composed of two sets of splines are worked out in the form of the values at ten domain points in each triangular cell, both of which possess distinct local supports. Furthermore, the explicit coefficients in terms of B-net are obtained for the two sets of splines respectively.     

A SPLINE METHOD FOR SOLVING TWO-DIMENSIONAL FREDHOLM INTEGRAL EQUATION OF SECOND KIND WITH THE HYPERSINGULAR KERNEL

1. IntroductionIn recent years, the boundary element methods became a reliable and powerful numerical methods for solving the boundary value problems, such as elastoplasticitys etc. In thesemethods, the original problem is reduced to a boundary integral equation. For the one dimensional boundarys a lot of methods have been put forward recently. But for the two dimensionalboundary situation, it is not so easy to be done because the partition can be very complicated.Since P. Zwart obtained an …     

AN INTERPOLATION METHOD BY BIVARIATE CUBIC SPLINES WITH C~2 -JOIN ON TYPE-II TRIANGULARS AT A RECTANGULAR DOMAIN

In this paper, an interpolating method for bivariate cubic splines with C2-join on type-II triangular at a rectangular domain is given, and the approximation degree, inter-polating existence and uniqueness of the cubic splines are studied.     

An interpolation method by bivariate cubic splines with <Emphasis Type="Italic">c</Emphasis><Superscript>2</Superscript>-join on type-II triangulars at a rectangular domain

In this paper, an interpolating method for bivariate cubic splines with C ²-join on type-II triangular at a rectangular domain is given, and the approximation degree, interpolating existence and uniqueness of the cubic splines are studied. Supported by NSFC General Projects(60473130).     

一类三角剖分下样条空间S_3~1(Δ)维数

首次提出了一种判别样条空间S13(Δ)维数不依赖剖分几何性质的协调条件·　依此 ,在一类较一般的三角剖分下 ,获得了S13(Δ)的维数·     

凸正规上半连续模糊真值集上二型三角模的剩余算子

基于连续三角模的剩余蕴含,本文得到了凸正规上半连续模糊真值集上扩展算子(二型三角模)的剩余算子表达式,从而回答了文献[D. LI, Inf. Sci., 2015, 317: 259-277]的一个公开问题.     

依赖型值的非奇异自适应三角剖分方法

1 引言 众所周知,三角剖分是在许多科学计算如曲面设计与拟合、有限元计算以及其他大型科学计算等领域中不可回避的问题.