查询词典 initial approximation

The second part has summarized from the one-dimension and multivariate respects the abundant approximation properties of Bernstein polynomials, mainly including the estimation of approximation degree, derivative approximation, linear combination approximation and weighted approximation.

第二部分从一元和多元两个方面系统总结了Bernstein算子丰富的逼近性质，主要包括逼近度估计、导数逼近、线性组合逼近和加权逼近等。

The close relationship between the Hybrid polynomial approximation and the classical Hermite polynomial approximation to rational curves and surfaces are studied, Hermite approximation is in fact a special case of Hybrid approximation. The sufficient and necessary condition for the convergence of Hybrid approximation to rational Bézier surface is deduced and proved.

围绕着有理曲线曲面的Hybrid逼近，作者研究了有理曲线曲面的Hybrid多项式逼近与传统的Hermite多项式逼近之间的密切关系，并指出Hermite逼近事实上是Hybrid逼近的一种特例，此后演绎并证明了有理Bézier曲面的Hybrid多项式逼近收敛的充分必要条件。

More than 30 kinds of meshfree methods are reviewed in this paper in the light of weighted residual method, and different meshfree methods can be viewed as different forms of weighted residual method and/or with different approximation functions. Various kinds of meshfree approximate schemes are presented in detail, including moving least square approximation, kernel and reproducing kernel approximation, partition of unity approximation, radial basis approximation, radial point interpolation and natural neighbor interpolation.

详尽介绍了各种无网格近似方案(包括移动最小二乘近似、核近似和重构核近似、单位分解近似、径向基函数近似、点插值近似、自然邻接点插值近似等)和无网格法中常用的各类加权余量法(伽辽金格式、配点格式、局部弱形式、加权最小二乘格式和边界积分格式等)，并讨论了数值积分方法和边界条件的处理等问题。

ABSTRACT This paper summarizes our researches on two key techniques in curve and surface modeling-the geometric approximation techniques and the geometric interpolation techniques. The former includes three types of geometric approximation techniques: Hybrid polynomial approximation to rational curves and surfaces, offset curves and surfaces approximation, interval Bézier curves and surfaces approximation. The latter includes a series of algorithms for shape blending modeling: the MSI algorithm for shape blending between space polylines or trees, the MSI algorithm for shape blending between triangular meshes, and skeleton-based shape blending algorithms using triangular decomposition and star-shape decomposition.

本文是作者对曲线曲面造型中两类核心技术几何逼近技术和几何插值技术的研究成果的总结，其中前者包括有理曲线曲面的Hybrid多项式逼近、等距曲线曲面逼近和区间曲线曲面逼近等三类几何逼近方法；后者包括用于形状混合造型的几何插值方法的一系列算法：空间多边形形状混合的MSI插值算法、三角网格形状混合的MSI插值算法、树的形状混合的MSI插值算法以及基于骨架树形状混合的三角剖分算法和星形剖分算法。

The results indicated that when initial NO3--N was not leached, soil initial NO3--N and mineral N extracted by CaCl2 before aerobic incubation were closely related with raygrass nitrogen uptake, the correlation coefficients were 0.856 and 0.862, respectively, both reached at 1% significant level. When initial NO3--N was leached, it was no good relationship between mineralizable N extracted by aerobic incubation, soil initial mineral N and mineralizable N extracted by aerobic incubation, N0 and soil initial mineral N and N0 with raygrass nitrogrn uptake, the correlation coefficients were 0.410, 0.553, 0.492 and 0.419, respectively, indicating that the poor effects of mineralizable N on reflecting soil N capacity were influenced and disturbed by initial nitrate.

以包括土壤起始NO3--N盆栽试验植物吸氮量为参比，通气培养前CaCl2所淋洗起始NO3--N和起始矿质氮与5期黑麦草地上部氮素累积量密切相关，相关系数分别为0.856和0.862，达1%显著水平；与此相反，通气培养30周所矿化氮素、土壤起始矿质氮+通气培养30周矿化氮素、氮素矿化势(N0)及N0+起始矿质氮与5期黑麦草地上部氮素累积量间无显著相关关系，相关系数分别仅为0.410、0.553、0.492和0.419。

In this dissertation, the best simultaneous approximation with weight to infinite sequence from simultaneous-suns in complex normed linear space is considered, and in the case when the weight satisfies a certain condition, the characterizations of approximation from a simultaneous-sun and uniqueness of approximation from a RS-set are obtained; moreover, in the case when the weight is free, the characterizations of approximation to a totally bounded sequence from a convex set are established.

本文在复赋范空间中研究了同时太阳集对无限序列的加权同时逼近问题，在权满足一定条件时，通过把所研究问题转化为连续向量值函数空间中相应集对一个上半连续函数的最佳逼近问题，得到了逼近的特征和RS集逼近的唯一性定理，有例表明它们是已有结果的本质推广；在权不受限制时，得到了凸集对全有界序列逼近的特征。

First low order approximation of generating function and approximate optimal trajectory were obtained. Then using low order approximation of generating function of Hamilton "relative motion" to the approximate optimal trajectory, improvement of the approximate optimal trajectory was iteratively made. In this way, high order approximation accuracy can be obtained by only using low order approximation, which is much cost effective in computing.

首先以较低的计算代价，获得最优控制Hamilton系统生成函数的低阶近似，得到一条近似的最优轨线，然后将最优控制Hamilton系统相对于近似最优轨线求"相对运动"，该"相对运动"仍具有Hamilton性质，利用这一"相对运动"的生成函数低阶近似，可以对近似最优轨线进行迭代修正，从而以计算代价较小的低阶近似逼近计算代价高得多的高阶近似的精度。

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。

In generic mathematical approximation methods Chebyshev multinomial approximation algorithm has better effect on reducing approximation error. This paper brought forward a parallel Chebyshev multinomial approximation algorithm based on a unique representation of complex curve, and implemented the parallel program in two Java methods.

常用的数学逼近法中切比雪夫多项式拟和法误差较小，对此，提出一种基於复杂曲线表示的切比雪夫多项式拟合并行算法，并采用两种Java方案实现并行程序。

On moving base, a new initial alignment algorithm for strapdown inertial navigation system is proposed. In the algorithm, two special inertial frames, the initial-time inertial frame (i0 frame) and the initial-time SINS body inertial frame (ib0 frame), are defined and are selected as calculation reference frames, then, the calculation of initial alignment direction cosine matrix is expanded into three parts:(1) the DCM between i0 frame and the navigation frame will be easily obtained via local geographical coordinates and initial alignment time;(2) attitude updating using gyro samples gets the DCM between SINS frame and ib0 frame;(3) by explaining SINS specific force equation in SINS body frame, the relation between velocity log, accelerometer measurement and gravity acceleration is established to achieve the constant DCM from ib0 frame to i0 frame.

在运载体运动情况下，提出了一种适用于捷联惯导系初始对准的新算法，该算法以惯性空间为参考基准，即建立了初始时刻惯性坐标系（i0系）和初始时刻捷联惯组惯性坐标系（ib0系）两个惯性坐标系，将初始对准姿态矩阵的实现分解为三部分：（1）通过地理位置和初始对准时间求解i0系至导航坐标系的变换矩阵；（2）使用姿态更新算法实时计算捷联惯组相对于ib0系的变换矩阵；（3）通过惯导比力方程变形，获得测速仪辅助测量、加速度计输出和重力加速度之间的关系，从中可以求解出从ib0系至i0系的常值变换矩阵。

Pachomius manual labour was organized as an essential part of the monastic life; and since it is a principle of the monks as distinguished from the mendicants, that the body shall be self-supporting, external work of one sort or another has been an inevitable part of the life ever since.

根据圣pachomius体力劳动组织作为一个重要组成部分寺院生活；以来，这是一个原则的和尚，作为有别于乞丐，该机构应自支撑，对外工作的这种或那种已一个必然的一部分，生活至今。

In order to study the effects of parametrical rolling on the ship movement and tilts, in allusion to ship's navigating in regular following waves, the equation of ship rolling motion is transformed into normal Mathieu equation by proper variable replacement when strong parametrical excitation in restoring moment varied according to sine or cosine wave.

为研究参数横摇对船舶运动和倾覆的影响，通过对船在规则波上随浪航行时，恢复力矩中出现的1个以正余弦规律变化的强参数激励项进行适当的变量置换，将船舶的横摇运动方程转换成标准形式的Mathieu方程。