插值函数

The results showed that TPS was of the best accuracy of three methods for temperature, precipitation and relative humidity, significantly for air temperature and precipitation. The difference of the accuracy of three interpolation methods for the aestival relative humidity was not significant.

结果表明：薄盘光滑样条函数法的插值精度最优，特别是温度和降水的效果尤其明显；对于三种插值方法，相对湿度的插值精度在夏季差异不明显。

The main purpose is to construct cubature formulae on an arbitrary spherical triangle. Firstly a method for accurately computing the definite integral of spherical polynomial functions on a spherical triangle is proposed.

本文主要研究定义在球面三角形上函数的数值积分，通过积分的插值多项式函数构造具有多项式精度的插值型求积公式，以及给出精确计算球面三角形上多项式函数方法。

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。

The benefit of this method is its mathematical simplicity and its consequent ease in programming. Secondly, it brings out a new 3D interpolation method—hypersurface spline method, this method extends the surface spline method of 2D interpolation into 3D space.

其次，提出了一种基于超曲面样条函数进行三维空间插值的新的三维空间插值方法，该方法将二维的曲面样条函数插值法进一步拓展到三维空间。

There are substantial relation between the interpolation and approximation of functions.The interpolation polynomial is regarded as the important tool of achieving approximation of function.

函数插值与函数逼近有着密切的联系，插值多项式可看作实现函数逼近的一种重要工具。

The multivariate polynomial interpolation problem is a classical mathematical problem that is widely used in many fields, such as multivariate function list, surface design and finite element method. In recent years, multivariate polynomial interpolation has been focused by many people, of which the geometric topological struction of sets of interpolation nodes is also much concerned by us.

多元多项式插值问题是一个十分具有研究意义和实际应用价值的数学问题，它广泛应用于多元函数列表，以及曲面的外形设计和有限元法等诸多领域，近年来多元多项式插值越来越受到人们的广泛关注，其中有关插值结点组的几何拓扑结构问题也是人们十分关注的内容。1998年，梁学章和吕春梅在文献[2]中借助代数几何中的有关理论，进一步讨论了沿无重复分量平面代数曲线上的Lagrange插值问题，并应用Cayley ？

Then,we prove the convergence of the radial basis function for solving partial differential equations with projection methods .

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。

This thesis will be expanded from two aspects: first, delta-sequence obtained by cubic spline interpolation cardinal function showed the properties of symmetry, Riesz basis and interpolation. Non linear convection diffusion equation (Burgers′equation) was used as an example. Then we modified this delta-sequence to improve the attenuation, the same example was used in numerical application.

在小波方法与PDE算法相结合方面，本文主要从两方面入手：首先是以样条插值基函数为基础构造δ-序列核，以非线性对流扩散方程为例给出了一种数值算法；进而对三次样条插值基函数进行改进，构造新的具有更快衰减性质的δ-序列核，同样以非线性对流扩散方程为例验证了新函数在数值求解中的有效性。

And by using the initial conditions as well as the end conditions, the dynamic problem is then transferred to a second kind Volterra integral equation about the function of the axial strain with respect to time which can also be solved successfully by the interpolation method. For piezoelectric and pyroelectric hollow cylinders, by following the solving procedure for elastic hollow cylinder and by using the electric boundary conditions, the dynamic problems are transferred to two Volterra integral equations about two functions of time, one is axial strain and the other is related to electric displacement, which can also be solved efficiently and quickly by employing interpolation method. The elastodynamic solutions of hollow spheres, which are made of elastic, piezoelectric and pyroelectric materials, respectively, for spherically symmetric problems are also obtained.

对于弹性空心圆柱，通过引入一特定函数将非齐次边界条件化为齐次边界条件，然后利用正交展开技术，导出关于时间函数的方程，再结合初始条件和端部边界条件，将原问题转化为关于一个时间函数的第二类Volterra积分方程，运用插值法可给出此积分方程的解；对于压电和热释电空心圆柱，利用求解弹性空心圆柱相似的方法，再结合电学边界条件，原问题转化为关于两个时间函数（轴向应变和与电位移有关的函数）的第二类Volterra积分方程组，同样可用插值法来构造相应的递推公式高效地求解此积分方程组。

Average annual precipitation data of the last 30 years from 1961 to 1990 at 186 meteorological stations in Gansu and its nearby regions was compared and analyzed by Inverse distance weight tension, Spline, Ordinary Kiging methods. The result showed that the three interpolators could reflect the spatial distribution of precipitation of Gansu province. Ordinary Kriging method was the most effective, followed by Spline methods and Inverse distance weight tension method.

利用甘肃及其周边186个气象台站30年平均降水资料，分别采用了反距离加权法(In-verse distance weight tension)、样条函数法和普通克里格法等3种常见的空间内插方法较为系统的分析比较了这3种内插方法插值结果，结果表明：3种方法的结果都基本上反映了甘肃降水大体空间分布规律，而普通克里格法的插值效果最好，样条函数法次之，反距离加权法较差。

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