数值稳定性

Considering the numerically more stable properties of Normal Equation with Constraints and Hachtel's augmented matrix method for SE, all telemetered and virtual measurements are classified reasonably. Using blocked and sparse matrices technology, a new SE algorithm with computing speediness and numerical stability is proposed.

借鉴WLS估计中带等式约束的正规方程法和Hachtel法数值稳定性更强的优点，将遥测量和虚拟量测合理分类，并采用分块和稀疏矩阵技术形成了一种计算速度快、数值稳定性好的状态估计改进算法。

Approximating unknown function by barycentric Lagrange interpolation which has advantages of higher precision and good numerical stability, the barycentric interpolation collocation method for analyzing deformation and buckling load of ring is presented.

采用数值稳定性好、计算精度高的重心Lagrange插值近似未知函数，提出数值分析圆环变形和临界载荷的重心插值配点法。

Based on a formal analysis of lifting decomposition, the hierarchical structure concept of the decomposition set, as well as the lifting decomposition technique of the polyphase matrix' greatest mth-order common divisor, is proposed to conquer the difficulties in the practical computation of and the optimal search in the huge decomposition set.

本文在形式化分析Lifting分解原理的基础上，提出了分解集合的分级结构概念以及多相矩阵的m阶最大公因子Lifling分解技术，克服了分解集合求解问题的高复杂性所带来的实际计算与搜索困难；进一步地，从数值稳定性及计算代价两方面研究了分解的评价问题，设计出两种实用的分解稳定性准则；最后，结合分级结构技术提出一种最优分解算法。

Keywords: Delay differential equation;Numerical method;Numerical stability

中文关键词：延时微分方程；数值方法；数值稳定性

The GKS stability theorem for one-dimensional model of hyperbolic initial and boundary value problem, Trefethen's explanation and extension based on the concept of group velocity are generalized firstly. Another possible high-frequency instability mechanism in numerical realization of MTF is pointed out based on his explanation and extension, namely, coupling effect of outgoing harmonic wave along one direction and node motion in the other directions can reverse the energy propagation in multi-dimensional discrete grids.

本文概述了—维双曲型偏微分方程组初边值问题数值稳定性的GKS定理及Trefethen基于群速度概念对这一定理的解释和推广；并应用Trefethen的解释和推广指出了MTF在数值实现中可能出现的另一种高频失稳机制，即在多维离散网格中，沿某一空间方向的外行简谐波，由于与其他空间方向节点运动的耦合效应可以使能量传播方向反向。

It has characters of succinct working environment, good numerical stability and abundant function resources.

MATLAB是一种高性能的数值计算的科学计算语言，具有程序开发环境简洁直观、数值稳定性好、函数资源丰富的特点。

Numerical algorithms process doesn't depend on initial. It has good numerical stability.

数值求解过程没有初值依赖性，具有很好的数值稳定性。

Theoretical analysis and numerical results show that the new reconstruction algorithm can reduce the computational complexity and greatly improve the numerical stability.

理论分析和数值试验都表明，这种新的重建算法较常用的Newton-Raphson类算法，不仅数值稳定性有较大的提高，而且计算量有所减少。

Moreover, some results about the stability of different numerical methods for the delay system are also itemized.

进一步，又对各种计算方法的数值稳定性进行了回顾，概述了各种常用的数值方法求解延迟微分方程所取得的理论结果。

We analyze theoretically the various algorithms of the fundamental matrix, and suggest that the input data should remove the errors in measurements through pre-processing for the algorithm stability. The robust algorithms, the cross-ratio based algorithm and the regularized pre-revised algorithm, are presented.

通过对目前常用算法分析及数值模拟指出，要提高算法的数值稳定性，最有效的办法是直接对输入数据作预处理去除噪声，并给出了较为鲁棒的基于交比预处理算法，和正则化预处理算法。

This one mode pays close attention to network credence foundation of the businessman very much.

这一模式非常关注商人的网络信用基础。

Cell morphology of bacterial ghost of Pasteurella multocida was observed by scanning electron microscopy and inactivation ratio was estimated by CFU analysi.

扫描电镜观察多杀性巴氏杆菌细菌幽灵和菌落形成单位评价遗传灭活率。