线性代数

In the first part, considering a linear dynamic system, system's differential algebraic equations are converted into algebraic equations using Simpson's integration rule, which can be solved easily by the steady-state data reconciliation theories for this dynamic data reconciliation problem.

在第一部分，考虑线性动态系统情况下，以辛普森积分法将系统动态方程式转换成代数方程式，接下来可利用稳态数据调和理论解决此动态数据调和的问题。

With the development of science and project technology, more and more questions need the solution of big linear systems. This solution is one of the fastest ways for researching numerical algebra, especially for the big sparse matrix.

随着科学和工程技术的发展，越来越多的问题需要求解大规模的线性方程组，对这类方程的快速求解已成为数值代数研究的热点之一，特别是具有稀疏结构的大型方程组的求解。

By introducing the nonlinear complementarity problem function, the Karush-Kuhn-Tucker conditions of OPF model are transformed equivalently into a set of semismooth nonlinear algebraic equations. Then the set of semismooth equations can be solved by a semismooth L-M method based on the subdifferential. The method belongs to Newton-type method. It can ensure the positive defmitiveness of the iterative coefficient matrix by using the L-M parameter, which avoids the ill-conditioning of iterative equations. The method, requiring only the approximate solution of a linear system at each iteration, is quite applicable to the large-scale cases.

在利用非线性互补函数将OPF模型的KKT条件转化为半光滑非线性代数方程组后，采用基于次微分的半光滑L-M法求解，该方法属于牛顿法范畴，可通过对L-M参数的调整保证迭代系数矩阵的正定性，克服了系数矩阵的奇异引起的"病态"，且该方法在确定搜索方向时只需求解线性系统的加热器近似解，适用于大规模系统的求解。

This paper, based on the secong approach, presents a new efficient algorithm to design symmetric bi-orthogonal M-band wavelets with arbitrary regularity by using Grobner basis and syzygy module algorithm in computing algebra, which bi-orthogonalizes the polyphase matrix line by line.

本文基于第二种思路结合计算代数中Groebner基和合冲模的思想和算法提出了一种同时具有任意正则阶和线性相位性质的M带双正交小波的新型高效构造算法，其中采用多相位矩阵逐行双正交化的方法。

In recent years, the trace function, as a linear transform from an extension victor space to its basic victor space, has been comprehensively employed to do researches concerning the algebra construct

近年来，迹函数作为一种从扩域向量空间到其基础域向量空间的线性变换，被广泛用于研究有限域的代数结构及序列密码的性质。

The first-order of the modal flexibility for a real symmetric undamped structure with distinct eigenvalues was derived based on an efficient algebraic method. The formulae are simple and compact, and it is easy to program. Moreover, it only requires one eigenvector to be known to calculate the sensitivity of modal flexibility.

代数方法解析推导出无阻尼线性系统模态柔度一阶灵敏度的解析表达式，该表达式简洁紧凑，便于编程，而且在计算阶模态柔度的灵敏度时，只需一阶模态信息，具有显著的优点。

We first show that the multiple harmonic Ritz values have only one harmonic Ritz vector associated with them in algebra.

用代数方法证明对每个重调和Ritz值，只有一个线性无关的调和Ritz向量与之对应。

The theory of vector space is an important and extensively applied algebraic branch of which matrix is one of the most important tools.

一个重要的有广泛应用的代数分支是线性空间理论，矩阵是其中最重要的工具。

In several recent years, the linear encoding algorithm of the LDPC codes has also met with success. But the algebraic structure and algebraically constructing method of LDPC codes have still many problems need to be researched.

近年来LDPC码的线性复杂度编码算法有所突破，但它的H矩阵的代数结构及其构造方法，还有许多问题尚待研究。

The generalized criterion for minimum zone in the determination of form error of surface is presented on the basis of linear minimax techniques, and the criteria of such surfaces as for cylindricity and straightness with arbitrary direction are derived from this generalized criterion.

本文讨论形状误差最小区城的判别准则和判别方法。根据线性极差极小化问题解的特征，给出形状误差最小条件的统一判别准则。推导出各种形状误差最小区域判别法(包括圆柱度误差和任意方向直线度误差)，并在几何判别的基础上得出代数判别的格式。

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。