系数矩阵

This thesis consists of two parts. The first one was that boundary value problem was discrete with five point difference method. Three kinds of memory formats were studied, which were full matrix, half band width and row compress sparse. Full matrix memory format and half band width memory format first was contrasted. The results show that half band width has efficiency in space. Then the algebraic system of finite element method was solved by Gauss-Seidel iteration method to popular row compress sparse memory format.

本论文由两部分组成，第1部分针对边值问题，用5点差分格式进行离散，并对离散矩阵这类大型稀疏矩阵，研究了系数矩阵的3种存储格式的优劣，即：满矩阵存储格式、半带宽存储格式和按行压缩稀疏存储格式，首先我们将满矩阵存储方式和半带宽存储格式进行了对比，迭代法的数值实验表明：利用半带宽存储的矩阵在空间运算方面具有高效性；然后针对目前数值实验中流行的按行压缩稀疏存储格式，实现了有限元离散代数系统的迭代法的求解。

In this paper another deductive proof of the algorithms for the recursive solution of the system of linear equations with a Toeplitz coefficient matrix is considered, and formulas for the specific recursive solution of the various forms of the system of linear equations in accordance with a Toeplitz coefficient matrix are given.

本文给出了具有托布里兹系数矩阵线性方程组递推解法算式的另一推导证明方法，并给出了基于托布里兹系数矩阵的各种线性方程组的具体递推解法公式。

The very important part for wave tomography is to get coefficentmatrix of tomography equations, that is the Jacobin matrix, or deviationderivative matrix of wave field to physical parameters.

波动成像最关键的一步就是求取成像方程的系数矩阵，也就是雅可比系数矩阵，也即波场对物性参数的偏导数矩阵。

The Reflexive Solutions Of The Matrix Equation discusses the solutions that satisfies or, and it is called reflexive solutions.

本文利用矩阵方程的系数矩阵秩的关系、矩阵的运算、矩阵的分块及矩阵的广义逆等，给出矩阵方程有解的条件、解的个数及解的结构。

The algorithm has following properties: Although the merit function has the form of least squares of a system of overdetermined equations, in the Newton equation of our algorithm, only the coefficient matrix of the system of overdetermined equations is used instead of its product as in Guass-Newton method for solving the least squares problems. That is, our Newton method is more like that for the system of nonlinear equations rather than that for LSPs. The global convergence is obtained for VLCP with vertical block P_0 + R_0 matrix; The local quadratic convergence rate is proved under the condition that the solution is BD-regular; Although there is only a Newton equation in our algorithm, the finite convergence property can be shown if matrix is vertical block P— matrix (without the hypotheses of strict complementarity).

该算法具有下列特点：所构造的价值函数虽然具有超定方程组的最小二乘问题的形式，但在基此建立的Newton算法中，其Newton方程的形式更象非线性方程组的Newton法中的Newton方程，仅利用了超定方程组的系数矩阵本身的信息，避免了一般最小二乘问题的Guass-Newton法中必须计算系数矩阵的乘积的工作量；对竖块P_0+R_0矩阵的垂直线性互补问题，算法具有全局收敛性；在解是BD-正则条件下，证明了算法的局部二次收敛性；虽然算法只含一个Newton方程，但对竖块P-矩阵垂直线性互补问题，算法具有有限步收敛性。

A bstract: This paper focus on virtual instrument design of modal parameters identification with curve fitting theory based on rational fraction orthogonal polynomials. Using Forsythe orthogonal polynomials solves the coefficient equation instead of normal power polynomials in order to decrease the morbidity of it, making the orders of coefficient equation reduce to half and increasing computing efficiency.

本文基于有理分式正交多项式曲线拟合理论对振动系统的模态参数辨识进行了虚拟仪器的设计，为了减少系数矩阵的病态，采用 Forsythe 正交多项式代替普通的幂多项式进行求解，使系数矩阵阶次降低近一半，提高了运算速度。

Firstly, the coefficient matrix is put into Excel so as to see the possible solution to the linear equation groups; then the reciprocal matrix of the coefficient matrix is obtained; lastly the solution to the linear equation group is gotten.

首先在Excel中输入系数矩阵，并判断线性方程组是否有解，然后求出系数矩阵的逆矩阵，最后求出线性方程组的解。

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。

Aim at the false-solutions(the meaning is the solutions do not satisfy the divergence theorem) of FEM, impose the magnetic divergence conditions

针对有限元数值解中存在的伪解问题(即求出的解不满足相应的散度条件)，推导出了强加散度条件的磁场有限元系数矩阵的表达式，本文混合法中的有限元系数矩阵即是在此基础上形成的。

In this paper, the following progress has been discussed:(1) the improved conjugate gradient algorithm which combines the inversion equation;(2) the formulation for velvet gene at all directions and the approximation method of Jacobian matrics based on disturbance method;(3) the model is adjusted by analyzing the influence of damp coefficient and correction factor to inversion result ;(4) the influence of damp coefficient to the resolution of inversion is studied. to some degree, we improved the problem of "barycenter ascending shift" to electric anomalous body in 3-D resistivity inversion.

本文主要讨论了以下几个方面的内容：（1）结合反演方程式改进的共轭梯度算法；（2）基于扰动法的线源Jacobi矩阵的近似计算方法及光滑系数矩阵在各个方向上的光滑因子的计算公式；（3）通过分析阻尼系数与修改量校正量对反演结果的影响，提出了利用校正系数对模型修正量进行校正；（4）较为系统的讨论了阻尼系数λ对反演分辨能力的影响，较好的改善了三维电阻率反演中的电性异常体重心的&上漂&现象。

But we don't care about Battlegrounds.

但我们并不在乎沙场中的显露。

Ah! don't mention it, the butcher's shop is a horror.

啊！不用提了。提到肉，真是糟透了。