插值法

In this dissertation, the following critical theoretical problems on local La-grangian numerical differentiation are studied: explicit formulas, local estimate for the remainder, and the highest order of approximation in the case that the values of the function at these interpolation nodes have perturbationsLagrangian numerical differentiation is a method that the Lagrange interpolation polynomialis differentiated to approximate the derivative, where Tn ={t_0,t_1,......

本文主要研究有关局部Lagrange数值微分法的一些关键性的理论问题：公式的显式表示，余项的渐近估计，以及在插值数据有扰动的情况下，局部Lagrange数值微分法的最大逼近阶。

In this paper,using the improved L-P method and the interpolation perturbation method,the authors seek to solve a class of the damped strongly nonlinear free oscillation problems.

文摘：本文用插值摄动法及改进的L-P法相结合的方法求解了一类有阻尼的强非线性自由振动问题，得到了一级近似解。

Based on the good essential boundary condition processing capability of radial point interpolation meshless method, as well as the better computing efficiency of Element-free Galerkin method, the mixed method coupling EFG and RPIM is used to deal with the essential boundary condition.

基于径向基点插值无网格方法良好的本质边界条件处理能力，以及无网格伽辽金方法较好的计算效率，应用混合元法耦合两种无网格方法进行了本质边界条件的处理，数值算例结果表明：混合元法简明有效，计算概念清晰，易于编程计算。

Due to the limited number of measurements on the response data, both Kalman Estimator technique and Singular Value Decomposition incopoerated with piecewise cubic Hermite Polynomial curve fitting method are used to reconstruct the unmeasured reponses and establish the full response measurement.

由於有限的量测资料，本文介绍卡氏重建器与结合分段式立方Hermite型插值多项式之奇异值分解重建法，以重建未量测点之反应历时，以利进行部分量测系统之外力识别。

Based on the Maxwell\'s equations, the boundary value problem, variation problem, interpolation function and stiffness matrix in two-dimensional magnetotelluric are derived.

从麦克斯韦方程组出发，推导出二维大地电磁测深的边值问题、变分问题、有限单元法的插值函数以及单元刚度矩阵。

This book reviews the many areas of numerical analysis, including the configuration polynomial, finite difference, factorial polynomials, summation, Newton formula, operator and configuration polynomial, Cheung section, close polynomials, TaylM more item type, interpolation, numerical differentiation, numerical integration, and with the series, differential equations, differential equations, least squares polynomial approximation, minimax polynomial approximation, rational function approximation, triangular approximation, non-linear algebra, linear equations, linear programming, boundary value problems, MonteCarIo methods and so on.

本书综述了数值分析领域的诸多内容，包括配置多项式、有限差分、阶乘多项式、求和法、Newton公式、算子与配置多项式、祥条、密切多项式、TaylM多项式、插值、数值微分、数值积分、和与级数、差分方程、微分方程、最小二乘多项式逼近、极小化极大多项式逼近、有理函数逼近、三角逼近、非线性代数、线性方程组、线性规划、边值问题、MonteCarIo方法等内容。本书的特色主要表现在利用例题及大量详细的题解来透彻地阐明所述内容的内涵，同时附有大量的补充题以便读者进一步巩固和深化从书中获得的数值分析知识。

The Neumann boundary value prob-lem is firstly reduced into the equivalent natural boundary integral equation withthe kernel possessing 2nd-order singularity,and then the corresponding variationalproblem on the boundary is obtained.By applying Quak trigonometric wavelet basisBjsee(1.2.3as boundary elements and the method of expanding kernel functionto its Galerkin discretization,we obtain simple computational formulae of the en-tries in the stiffness matrix.

首先，我们将Neumann边值问题归化为等价的带有2阶强奇性核的自然边界积分方程，然后化为边界上相应的变分形式，以Hermite插值Quak三角小波基Bj见(1.2.3作为边界元并利用积分核函数展开法将其离散，得到了十分简单的刚度矩阵系数的计算公式，而且刚度矩阵具有十分简单的形式，它是分块循环对角阵。

We constructed a finite volume scheme of fifth order Hermite type with high accuracy for twopoint boundary value problems, choosing trial and test spaces as the fifthorder finite element space of Hermite type and the piecewise linear function space respectively. We didn't use higher derivatives as interpolation conditions, which is the same as the thirdorder finite element of Hermite type, but the scheme obtained had higher accuracy.

构造求解两点边值问题的一种Hermite型五次元高精度有限体积法，其中试探函数空间取Hermite型五次有限元空间，与Hermite型三次元相同，未引入更高阶导数作为插值条件，检验函数空间取分段线性函数空间，这样构造的格式求解精度更高。

This thesis investigates the profile extraction and shape optimization on the result of topology optimization of planar compliant mechanisms. The main context includes the following work:(1) summarizing and analyzing the recent research status, some harvest and unsolved problems;(2) analyzing the conceptual design of planar path-generating compliant mechanisms and its mathematical model and tools;(3) Modifying the method of density contour as the method of profile extraction, and developing a method to optimize the density function in the profile extraction according to the requirement of the design of compliant mechanism;(4) developing a method to abstract the compliant mechanism into a form of links and joints by using the principle of connectivity on topology;(5) developing a method of shape optimization of planar path-generating compliant mechanisms, by representing the profile of the abstracted compliant mechanism as simple curves such as straight lines and arcs, establishing the models of the size optimization of the parameters of these curves, so that the compliant mechanism has a machinable shape;(6) At last, proving the feasibleness and effectiveness of the design method by making simulation design and validating it in FEA software.

主要工作包括：(1)分析了柔顺机构拓扑优化和形状优化的研究现状，分析了目前柔顺机构的研究重点、主要成果和尚未解决的问题；(2)分析了基于SIMP的柔顺机构概念设计方法及其相关工具和模型；(3)针对柔顺机构轮廓提取的特殊要求，提出了密度等值线法的改进方案，对密度函数插值点密度值进行优化，提出优化模型和选择优化算法；(4)根据轨迹输出平面全柔顺机构自身的形状特点，提出了轨迹输出平面全柔顺机构的抽象方法，即应用拓扑学上的连通性原理将柔顺机构抽象成杆件和结点形式，并对相应的数学原理进行了证明；(5)提出了平面全柔顺机构的形状还原和尺寸优化方法，对抽象的柔顺机构进行还原，将其轮廓还原成简单曲线的连接，从而建立尺寸优化模型，对机构进行尺寸优化设计，在得到可加工的机构轮廓的同时又能对关键部位进行特别处理；(6)进行了柔顺机构的数值仿真设计，并将所得设计结果导入商用有限元软件中进行仿真实验，证明了设计方法的可行性和有效性。

The scheme is verified by simulative signal, and then is applied to the denoising vibration signal of two mine ventilators.

介绍了基于插值细分法的第二代小波变换的基本原理和变换过程，给出了小波降噪的阈值选取方法。

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。