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Douglas and Russell first presented the idea of characteristics in[13],in whichthe diffusion term is included in the derivative of characteristic direction of the solu-tion and the backward difference quotient along the time axis was replaced by it alongcharacteristic direction.

Douglas,Russell[13]最先提出了特征法的思想,其主要特点是将模型方程的对流项隐含在解沿特征方向的导数之中,以沿特征方向的向后差商逼近取代通常方法中沿时间方向的向后差商逼近。

In the third chapter, we study the approximation and weighted approximation for a kind of generalized Baskakov operators of two-variable. Using different weight functions, we discuss the convergence on weighted space of polynomials and rate of convergence with Jacobi weight for this kind of two-dimensional product-type operators, which extends the results of one-dimensional operators.

第三章研究一类二元广义Baskakov算子的逼近及其加权逼近,主要针对于不同的权函数讨论了这类乘积型的二元算子及其导数在多项式权空间上的收敛性和加Jacobi权的收敛阶,把一元的结果推广到多元的情形。

Reduce the computing complexity of magnetic field integral equation with differential quotient, which makes the computing which combined field integral equation more efficiently.

在AIM算法的实现技术方面作了两个改进:一是采用了新的多极子展开方案,保证了迭代的数值稳定性;二是在差商逼近偏导数的过程中全部采用二阶形式,保证了差商逼近偏导数的精度。

Based on Bellman stochastic nonlinear dynamic programming, we develop an optimal control algorithm for the discrete stochastic system with conditional Markov structure.

基于Bellman随机非线性动态规划法,提出了具有条件马尔科夫跳变结构的离散随机系统的最优控制方法,应用随机变结构系统的性质对最优控制算法进行了简化处理,并将后验概率密度函数用条件高斯函数来逼近,针对一类具有条件马尔科夫跳变结构的线性离散随机系统,给出了其逼近最优控制算法。

Considering that the NURBS has become a standard in CAD/CAGD, we shall investigate the approximation to the solutions of the minimal surface equation with the tensor Bezier surface and B-spline surface.

首先我们讨论极小曲面的分片线性的逼近,由于NURBS已经成为形状描述的唯一工业标准,而且极小曲面本身至少应该是二阶光滑的,因此我们讨论了极小曲面方程的Bezier和B样条逼近。

The Hausdorff property of a kind of classifying mode is defined. And it is proved that the single-layer perceptron can deal with the classifying problems of any Hausdorff pattern sets. Chapter 5 studies the radial basis function networks and a proof of Cover pattern classifiable theorem is presented.

第四章主要研究多层感知机的万能逼近性和最佳逼近性,包括权值有界和隐单元权有界时的情况,定义了一种分类模式的Hausdorff性,证明了单层感知机能解决任意具有Hausdorff性的模式集的分类问题。

A new self-adaptive background approximating and updating algorithm based on optical flow theory is first presented in this paper.

在光流场等技术的基础上,提出了一种自适应背景逼近更新方法,以适应光线的变化以及噪声的影响;根据彩色差值模型计算当前帧图像和当前逼近背景图像的差分图像;并引入Gauss模型实现了运动目标的自适应阈值分割。

Cycloid cluster is a new concept presented in this paper, which is a set ofcycloids. To process the back-angle accurately and efficiently, the parameters ofcycloid are adjusted to make the envelope curve of cycloid approximate involute .

使用摆线簇包络线逼近渐开线是本文提出的一种新方法,摆线簇就是一组摆线,通过调整摆线簇中每条摆线的参数,可以使摆线簇中摆线包络线高精度的逼近渐开线,进而实现倒锥的加工。

As an updated multiscale geometric analysis tool, second generation Bandelets provide an optimal representation adaptively by multiresolution analysis and geometric directional analysis. In its realization, the search of optimal geometry directions that are as parallel to real geometries as possible is a critical step, which decides the performance and runtime of whole algorithm.

第二代Bandelets是一种新的多尺度几何分析工具,借助多尺度分析和几何方向分析自适应达到信号的渐进最优逼近,实现过程中最优逼近几何方向的寻找决定了整个算法的运行时间和性能。

A smooth approximation algorithm is then proposed based on hinge-finding algorithm via curved faces approximated to the hinging hyperplanes model, which can obtain a smooth approximation result and hold some good properties of hinge-finding algorithm such as simplicity and effectiveness.

本文对找链接算法做了两点改进,其一是扩充了链接超平面模型,在二维空间上弥补了链接超平面模型表示能力不足这一弱点。仿真实验显示使用扩充后的模型得到了更好的分片线性逼近结果。另一点改进是使用双曲光滑函数构造出了基于找链接算法的光滑逼近算法。理论分析证明了算法的可行性。仿真实验验证了理论分析。

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