插值函数

Algebraic curve is commonly used in CAGD. Traditional curve interpolation is in various forms of spline fuction. Although better result can be obtained by spline curve, the former two of elliptic, hyperbolic and parabolic shapes can not be represented by spline curve. An exploring research in this aspect is made in this thesis.

代数曲线是CAGD中经常用到的曲线，以往的曲线插值基本上是采用样条函数的形式，采用这种形式虽然能够获得很好的效果，但样条函数所能表达的形状都是抛物线型，对椭圆型与双曲线型曲线的表示是无能为力的。

Secondly, the asymptotic series are used to evaluate the density function of heavy-tailed Rayleigh distribution, and an efficient three-step method is proposed using the interpolating polynomial fit.

其次， 本文使用渐近级数计算拖尾Rayleigh分布的概率密度函数，基于插值多项式拟合，提出了高效计算密度函数的三步方法。

In this paper, based on the Bessel function, an Ordinary Differential Equation was derived for time-domain Green function and its gradients in this paper. A new efficient calculation method based on solving ODE is proposed.

在探索求解精度和计算效率的矛盾中，提出了结合求解常微分方程的节点制表、节点间插值的快速计算Gre en函数的方法并据此开发了一套三维深水时域Green函数的数值计算程序。

The present paper applies the quadratic splines to the Chemical Engigeering calculations for integration, interpolation and differentiation with good precision.

在样条函数的研究和应用日益广泛的今天，作者将人们所忽视的二次多项式样条函数引用到化工计算中的插值，求积和求导等方面，取得良好的结果。

Using cubic spline interpolation function, we construct a finite element model to approximate the nonlinear Schr〓dinger equation, and provide a complete discrete scheme with the conservation properties of mass and energy.

本章从应用角度出发，着重讨论孤波形式的解的计算，为此我们利用三次样条函数的插值基函数构造出非线性薛定谔方程的一个有限元离散模型，给出了具有保质量与能量守恒的全离散计算格式。

The case study shows that the shape functions and their derivatives of the meshless Kriging interpolation method have the properties of Kronecker delta function.

数值算例结果证明该法构造的形函数具备过点插值性质并且具有很好的曲线拟合特性，是一种非常好的无网格法形函数。

The shape function of the meshless local radial point interpolation method has the Kronecker delta function properties, and no additional treatment to impose essential boundary conditions.

无网格局部径向点插值方法的形状函数具有Kronecker delta函数的特性，便于施加位移边界条件，不需要进行特殊地处理。

The continuity and differentiability are achieved by using cubic polynomial interpolation based on hard thresholding.

用三次多项式在硬阈值的基础上插值，使新的阈值函数保持了连续性和可导性。

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。

Models of space variation were constructed at the directions of east-west and south-north based on the geostatistical method by using 10 survey data from the transplanting to ripening of the rice in Xiushan, Chongqing in 2008. Isoclines maps of the WBPH nymphs at each stage were created by the geostatistical software Surfer8.0 with Kriging interpolation.

本文根据2008年在秀山县的系统调查资料，运用地统计学中的半方差函数，建立了秀山县水稻栽插至成熟10次调查时间在东西和南北2个方向上白背飞虱若虫的空间变异曲线模型，并利用Surfer8.0软件对空间分布数据进行插值和模拟。

On the other hand, the more important thing is because the urban housing is a kind of heterogeneity products.

另一方面，更重要的是由于城市住房是一种异质性产品。

Climate histogram is the fall that collects place measure calm value, cent serves as cross axle for a few equal interval, the area that the frequency that the value appears according to place is accumulated and becomes will be determined inside each interval, discharge the graph that rise with post, also be called histogram.

气候直方图是将所收集的降水量测定值，分为几个相等的区间作为横轴，并将各区间内所测定值依所出现的次数累积而成的面积，用柱子排起来的图形，也叫做柱状图。