插值问题

In this paper we study the method of interpolation by radial basis functions in H~k(k ≥ 1) and give some error estimates. By means of such interpolation with a special kind of radial basis function, we construct a basis in H~k(k ≥ 1). Combined with the Galerkin method, this theory can be applied to solve boundary value problems for elliptic partial differential equations (such as the third boundary value problem for Poisson equation and the corresponding problem for the biharmonic equation), and some numerical experiments are also given.

本文从求解偏微分方程的角度出发，在被逼近函数u属于一般的Sobolev空间H~k(k≥1)的情形，引入了一种径向基函数插值方法，并建立了相应的误差估计；再利用这种插值性质，从一类特殊径向基函数出发构造Sobolev空间的一组基，针对Poisson方程第三类边值问题和重调和方程类似边值问题，为用无网格算法求解偏微分方程边值问题建立了相应的理论，并通过算例来验证了这一算法。

The second chapter is the main part of this paper, in which the formulation of the Riemann boundary value problem of non-normal type on the real axis, the solution method of homogeneous problem, the relation between the two kinds of different derivatives and the inhomogeneous problem will be thoroughly given. In this paper, the solution and the solvability of the Riemann boundary value problem of non-normal type on the real axis will be given. Furthermore, it is shown that the twokinds of derivatives of the function Ψ are existing and equivalent in the case ofthe solution about the original problem, therefore, we get uniformly Hermite interpolatory polynomial. The relation between the two kinds of different derivativesof the function Ψ are similar for smooth closed contours by means of the same proof.

第二章是本文的主要部分，分别给出了实轴上一类非正则型Riemann边值问题的提法、齐次问题的解法、两种导数的关系及非齐次问题的求解，本文运用杜金元教授[11]的方法获得了实轴上非正则型Riemann边值问题的封闭解及可解性条件，且在问题可解的情况下论证了函数Ψ的非切向极限导数和Peano导数存在且相等，从而获得了统一的Hermite插值多项式，同样关于封闭曲线上非正则型Riemann边值问题，采用本文论证方法证得了函数Ψ的非切向极限导数和Peano导数存在且相等，从而较好地统一了[10]、[11]中的Hermite插值多项式。

There exists one and only one solution with rank not greater than j to the rational interpolation problem with j interpolating points, which has at least one complementary solution The Welch-Berlekamp algorithm is a iterative algorithm.

本文的主要结果是： 1。利用初等的数学方法研究了有理函数插值问题的性质，证明了Welch-Berlekamp算法的有效性。

OpenGL-based VC, cassini elliptic function of the contour generation, isogram involving interpolation.

基于VC+OPENGL，关于cassini椭圆函数的等值线生成，涉及等值线插值问题。

Boundary polynomial point interpolation mesh-free method and boundary radial point interpolation mesh-free method were presented, based on polynomial basis and radial basis respectively for transient eddy current analysis, and their interpolation shape functions satisfy the Kronecker delta function and the essential boundary conditions can be directly imposed on the boundary nodes. An example on analyzing transient eddy current of a square metal column was set to prove the validity of the proposed methods, and a comparison on accuracy between BPPIM and BRPIM was analyzed as well.

运用多项式点插值法和径向基点插值法构造形函数，推导了适合于工程电磁场瞬态涡流问题的多项式基点插值边界无单元方法和径向基点播值边界无单元方法，这两种方法的空间插值形函数满足Kronecker delta条件，从而强加边界条件可以直接施加在边界点上，以金属长方柱的瞬态涡流分析作为数值算例，证实了两种方法的正确性和有效性，并对两种基类的点插值法进行了精度分析和比较。

Secondly, C1 Hermitian interpolation with spherical PH curve is discussed.

讨论了球面上PH曲线的C~1Hermite插值问题。

Computer-simulation results related to the TNN model substantiate that the timing neural network could handle well the inverse-interpolation problems of one-to-one and multiple-to-one mappings. Keywords: neural networks, weights direct determination, inverse problems, timing neural network

基于前面提出的网络模型，本文进一步提出一种增加时序控制条件的神经网络，即时序神经网络模型，并给出理论推导和进行仿真验证，结果表明该时序神经网络能够成功解决一一映射及非一一映射反插值问题。

From the above papers ,The problem about Hermite trigonometric interpolation on different trigonometric function spaces is always ignored.

从现有文献看，各个不同三角函数空间上的三角Hermite插值问题一直被人们忽略。

First, we introduce the definition of Full Hermite interpolation and the Vandermonde matrix, and two lemmas which are most important for solving the problem.

首先介绍了完全Hermite插值问题和有重Vandermonde矩阵的定义，并介绍了两个重要的引理。

The problem of constructing the planar C^1 cubic PH splines is discussed.

讨论了平面上三次PH曲线C^1 Hermite插值问题。

It has been put forward that there exists single Ball point and double Ball points on the symmetrical connecting-rod curves of equilateral mechanisms.

从鲍尔点的形成原理出发，分析对称连杆曲线上鲍尔点的产生条件，提出等边机构的对称连杆曲线上有单鲍尔点和双鲍尔点。

The factory affiliated to the Group primarily manufactures multiple-purpose pincers, baking kits, knives, scissors, kitchenware, gardening tools and beauty care kits as well as other hardware tools, the annual production value of which reaches US$ 30 million dollars.

集团所属工厂主要生产多用钳、烤具、刀具、剪刀、厨具、花园工具、美容套等五金产品，年生产总值3000万美元，产品价廉物美、选料上乘、质量保证，深受国内外客户的青睐