Regard appropriate development of the coal industry as the starting point in the thesis , , in analysis at the f our country coal characteristic and coal industry with the other economic foundation that technology get in touch of industry of industry in an all - round way , set up optimize models of industry of coal based on dynamic input - output analysis , and use the econometrics method to confirm the systematic parameter of this model , had asked the model of solving and analysis , applying theory and method of markov probability model modify and forecasting direct consume coefficient matrix in coal industry , and has probed into in the course of revising the parameter changes the influence caused toward other input - output index 论文中以煤炭产业的适度发展为出发点，在全面分析了我国煤炭产业的特点以及煤炭产业与其他产业的经济技术联系的基础上，建立了煤炭产业多目标动态投入产出优化模型，应用计量经济学方法确定了该模型的系统参数，求解模型并对最优解进行了分析，应用马尔科夫概型修订直接消耗系数矩阵以反映煤炭消耗的变化，并探讨了在修订过程中参数变化对其他投入产出指标所造成的影响。
The characteristics of different parallel algorithms are compared in accordance with the specialty of coefficient matrix of vibration equations of wheel / rail system . then , four parallel algorithms are used to solve the linear equations , such as gaussian elimination , lu decomposition , ldr decomposition and wz decomposition . with the method of cyclic distribution , all rows of the coefficient matrix is allotted into different processes , then eliminated and decomposed by relevant processors 针对轮轨系统振动方程组系数矩阵的特点，分析了现有各种求解线性方程组并行算法的优缺点，选择高斯消去法、 lu分解、 ldr分解和wz分解法作比较，采用循环带状划分的方法将系数矩阵的各行分配到各进程，由各个处理器完成所分配矩阵行的消元和分解。
Instead , there needs to store only the original coefficient matrix , some auxiliary matrices for the preconditioner and several vectors in the iteration methods . further , the core of the iteration is the matrix - vector multiplication and the solution of the auxiliary equations corresponding to the preconditioner . if the solution of the auxiliaries spend not very much , the computational cost in each iteration step will be very cheap , due to the fact that the sparsity of the matrix can be exploited sufficiently 与直接法相比，迭代法只需存储原系数矩阵、对应于预处理的几个辅助矩阵与少量几个向量，且迭代中除求解辅助线性方程组外，其余的计算主要是稀疏矩阵与向量乘积，从而能充分利用稀疏性减少计算量，但迭代法的收敛速度一般与系数矩阵的谱分布有关。
For both methods , at most two reduced linear systems of equations with the same coefficient matrix need to be solved in order to get iterative directions at each iteration and the iterative matrix involves only constraints in the working set , whose cardinality are much less than the number of original constraints 在其每次迭论文摘要代中，只有有效工作集中的约束参与计算。在本文中，我们在facchinei一fischer一kanzowkkt点有效约束集识别技术的基础上提出了三个具有强收敛性的qp一free算法。
Through ( multi - level ) bordered block partition of the power system topology matrix , a bbdf coefficient matrix which is suitable for above decomposition is formed . when the equation is solved with parallel iterative method , convergence acceleration is achieved through damping newton method 通过采用(多重)对角加边的方法进行电力网络拓扑分割,以形成适合以上分解法求解的对角加边形式的系数矩阵,并行求解后并对迭代过程进行阻尼牛顿法修正,以达到加速收敛的作用。
( 3 ) the re - orthonormalization technique is used to solve the loss of orthonormality of basis vector during the classical gmres method solving large - scale three dimensional elasto - static be problems . based on the characteristic of fundamental solution and the coefficient matrix , several precondition methods are studied . by using the technique of re - orthonoramalization and precondition , the practical gmres method is developed based on the classical one ( 3 )采用重正交技术解决了经典gmres方法在求解大型三维弹性静力边界元问题过程中出现的基向量正交性丧失的问题；结合边界元基本解和系数矩阵的特点以及并行化的要求，研究了几种预条件技术；并以重正交技术和预条件技术实现了经典gmres的实用化。
As we know not like with nonsingular linear equations , some singular linear equations are inconsistant . so we will deal with the two circumstances . among so many singular linear equations we are very interested in the equations whose coefficient matrices are range hermitian ( ep matrices ) 在众多的奇异线性方程组当中，一类其系数阵是值域hermite的奇异线性方程组引起了我们极大的兴趣，因为值域hermite的矩阵(也称为ep阵)以及与其相应的线性方程组很广泛地存在着。
The fast spot price solution proposed in this paper introduces a decomposing model , which is benefit for analyzing each component of spot price . based on interior - point optimal power flow , which has superiority on calculating and decomposing spot prices under power market environment , after rational approximation , the coefficient matrix and its factor table of modifying equation are made constant and need no recalculation during iterations 本文提出的快速实时电价算法采用适于对实时电价各组成部分进行分析的分解模型，在内点法最优潮流的基础上合理的常数化其修正方程系数矩阵，使其在每次迭代时不必重新计算，大大提高计算速度。
As to the former , we mainly use the definition of stability to prove it directly , first , analysing the eigenvalues of coefficient matrix of the stationary solutions in each subregion , then , affirming the existence and stability of the equilibrium point . for the latter , the complete stability is guarantee 对于前者，主要是直接运用稳定性的定义，分析各子区域定态解系数矩阵的特征值，然后再确定平衡点的存在性及稳定性。对于后者，则通过构造lyapunov函数来得到系统的完全稳定性。
To obtain the fast matrix - vector multiplication algorithm , we approximate the kernel function with piece - wise polynomial and get the approximate coefficient matrix a using the approximate kernel function . let n be the number of quadrature points and k2 be the number of interpolating knots at each subdomain . it is proved that the construction of a and the matrix - vector multiplication ax require o ( nk ) operations respectively 我们利用对核函数进行分片多项式插值逼近得到适用于快速方法的近似系数矩阵a ：矩阵a的计算和矩阵-向量相乘ax各需要o ( nk )次运算，存贮a需要占用o ( nk )内存，其中n为积分节点的个数， k ~ 2为每个小区域的插值节点数。
