插值问题

In this paper,some problems on bivariate Hermite interpolation by polynomial are studied.The concepts of strong H-basis and Hermite interpolation along a plane algebraic curve are proposed.

1引言如所知，光滑函数方法被广泛地应用于计算机辅助几何设计，有限元及散乱数据插值与拟合(Scattered data fitting and interpolation)等领域·在应用该方法过程中，有关光滑或Hermite插值格式及其显式表达式问题的研究是至关重要的一个方面。

Put the discrete algebraic equations of initial derivative conditions and algebraic equation system of governing differential equation together to form a new algebraic system.

采用重心Lagrange插值近似未知函数，推导了未知函数各阶导数微分矩阵的显式表达式，建立了求解二阶常微分方程初值问题的重心Lagrange插值配点法。

After briefly reviewing the classification and history of curve and surface modeling, we discuss the characters, applications and representative work on three types of geometric approximation. And we present a survey of the vertex correspondence problem and the vertex interpolation problem in 2D and 3D shape blending modeling and key frame animation.

作者简要回顾了曲线曲面造型的分类和发展历史，论述了曲线曲面造型中所遇到的三类几何逼近问题的特点、应用和代表性工作，并就用于二维和三维形状混合造型的几何插值方法从顶点对应和顶点插值两方面做了一个系统的综述。

So in this paper, first, the ELM is improved by taking the interpolation process under absolute coordinates, so that the horizontal interpolation could be taken in a horizontal plain of the same altitude, thus the problem of unreasonable interpolation sources is prevented.

所以本文首先对欧拉-拉格朗日方法作了改进，把其中的插值过程改在绝对坐标下进行，使得水平插值过程在同一高度的水平面内进行，从而克服了插值不合理的问题。

The traditional inverse distance weighted interpolation can not satisty the requirment of high accuracy because the atmospheric delay variation depends not only on the distance between the interpolated value and observations, but also on height difference.

针对反距离加权内插法在GPS大气延迟估计加密插值中存在的问题，提出了对样本点和待插值点间水平距离和高程差赋予不同影响因子的改进反距离加权内插法。

In this paper, the Lagrange interpolation formula asked a class function expression question, the determination function to the higher mathematics in the elementary mathematics in some value scope question, the equality proof question, the multinomial factorisation question, to ask to have the Finite series to pass the formula question, the certificate any n function at will n+1 different spots function value maximum value minimal problem and so on six aspects should serve as the simple introduction, and has separately made the comparison with these six aspects elementary mathematics method, thus solved some operation problems in elementary mathematics.

摘要本文对高等数学中Lagrange插值公式在初等数学中的求一类函数表达式问题、确定函数在某点的取值范围问题、恒等式的证明问题、多项式的因式分解问题、求有穷数列的通项公式问题、证明任一n次函数的随意的n+1个两两不同点的函数值的最大值的最小值问题等六个方面的应用作了简单介绍，并与这六个方面的初等数学方法分别作了比较，从而解决一些初等数学中的运算问题。

Firstly, the three-dimension boundary question and its corresponding variation question concerning the point-source electrical field on a 3-D structure are presented. Secondly, the finite element method is used to solve the variational equation. The study area is divided into many tetrahedral elements. Then, we interpolate with a tri-linear function in each element. So, the variational equation is converted into a linear equation system. Finally, taking into account saving of time, we make use of symmetric successive overrelaxation preconditioned conjugate gradient algorithm to solve large linear system, and obtain the potential value of each node, resulting in the calculation of the apparent resistivity values on the ground surface.

首先给出了三维构造中点源电场的边值问题以及相应的变分问题；然后利用有限单元法求解变分问题，采用四面体单元对研究区域进行剖分，在单元中进行三线性函数插值，将变分方程化为线性代数方程组；最后，考虑到节约计算时间，利用对称超松弛预条件共轭梯度迭代算法求解大型线性方程组，得到了各节点的电位值，进而计算出地表的视电阻率。

It offers the idea according to problem faced, considering the good character of the ends,the ajusted cubic B-spline curve is used to fit ship lines.it finds out the control vertexs according to a sequence of given points,and then, through particular formula,each point in the curve could be worked out.

针对面临的问题，提出了自己的思路，在数学计算方法上，由于三次准均匀B样条曲线良好的端部性质，这里用它来拟合船舶型线，首先根据所给的初步型值求出其控制顶点，然后根据相关公式进行插值便能得到曲线上的所有插值点。

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。

In order to deal with the numerical stability of convection dominated problems, using the local upwinding weight function, the upwinding local radial point interpolation method is proposed based on the local radial point interpolation method, and were then compared with those numerical results of the LRPIM.

为处理对流扩散问题中对流项占优时的数值稳定性问题，采用局部上风式权函数，在局部径向基点插值无网格法基础上构建了上风式局部径向基点插值无网格法。

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