迭代法

Convergence of semi-iterative method was discussed by Varga, Young and HU Jia-gan when iterative matrix is symmetric. In this paper, using Chebyshev polynomial and its properties, we obtain the convergence of semi-iterative method for a class of antisymmetric iterative matrix.

本文依据Varga， Young，胡家赣书中介绍的迭代矩阵为对称阵时，半迭代法的收敛性的理论，以Chebyshev多项式及其基本性质作为基本工具，对一类反对称迭代矩阵，研究其半迭代法的收敛情况。

By For the Jacobi iterative method of Gauss - Seidel iterative method and the comparison Initial research iterative equation and the nature of the coefficient matrix iteration convergence speed impact.

本文通过了举例对Jacobi迭代法和Gauss-Seidel迭代法进行了比较，研究迭代初值和方程组系数矩阵性质对迭代法收敛速度的影响。

Direct method of Gaussian elimination, Gaussian main-element elimination, and the iterative method of Jacobi iteration, Gauss - Seidel (Gauss - Seidel) iterative method is linear equations numerical solution of important ways.

直接法中的高斯消去法、高斯列主元消去法，以及迭代法中的雅可比迭代法、高斯-赛德尔（Gauss-Seidel）迭代法又是线性方程组数值求解的重要方法。

In the end, an example was used to demonstrate. Results indicate that Gauss-Seidel method and SOR method are move valid than Jacobi method, and SOR method is the best one.

最后，作为演示我们将迭代法，迭代法和迭代法用一个例题进行了比较，数值实验表明，迭代法和迭代法比迭代法更有效，而超松弛迭代法更优。

Firstly, the principle of the iteration method is presented, the characteristic of the method is analyzed. The downward continuation computation for model and practical data with noise of different variance is performed by means of iteration method.

首先介绍了迭代法的基本原理，分析迭代法的特点；然后利用迭代法对不同噪声水平的模型数据和实测数据进行向下延拓计算，研究噪声对迭代法的计算误差影响。

Missirlis in article [1]. At the same time, a sufficient condition for convergence of the PSD method is given to be compared when the coefficient matrix A of the linear system Ax = b is a symmetric, positively defective matrix. In §3.2, an example is given to state that the range of our sufficient condition is wider than theorem 3.3 of article [1]. On the other hand, following a.n analogous approach of [14] and starting the functional relationshipwe have a perfect analysis for the PSD method to converge and optimum valves for the involved parameters under different conditions.Under the assumptions that A is a consistent ordered matrix with nonvanishing diagonal elements and the eigenvalues of the Jacobi matrix of A are real,we get necessary and sufficient conditions for the PSD method to convergence.The result is equal to theorem 1 of article [9].Under the same condition, we can see the optimal parameter and of corresponding spectral radius of thePSD method in [8]:(2)When A is a consistent ordered matrix with nonvanishing diagonal elements and the eigenvalues of the Jacobi matrix of A are imaginary or zero,we get necessary and sufficient conditions for the PSD method to convergence.In chapter 3, the optimal parameter and of corresponding spectral radius of the PSD method are given by table 3.3. Moreover, under the assumption 0

Missirlis在文献[1]中定理3.3的不准确，同时给出了当线性方程组Ax=b的系数矩阵A为对称正定阵时，PSD迭代法收敛的一个充分条件与之比较，并且在§2.3中用实例说明了对于一部分矩阵而言本文得到的充分条件广于[1]中定理3.3的充分条件；另一方面，按照文献[14]的方法，我们从PSD迭代法的特征值λ与其Jacobi迭代矩阵B的特征值μ的关系式：出发，在不同条件下对PSD迭代法的收敛性和最优参数以及最优谱半径进行了完整的分析：(1)在系数矩阵A为(1，1)相容次序矩阵且对角元全不为零，其Jacobi迭代矩阵B的特征值全为实数的条件下，给出了PSD迭代法收敛的充分必要条件，此结果与[9]中的定理1等价，此时最优参数及最优谱半径由[8]得：(2)第三章表3.3中给出了，当系数矩阵A为(1，1)相容次序矩阵且对角元全不为零，其Jacobi迭代矩阵B的特征值全为纯虚数或零时的PSD迭代法的收敛范围和最优参数，并且我们可以得到当0

Exive least-squares solutions, antire?exive least-squares solutions, bisymmetric least-squaressolutions, symmetric and antipersymmetric least-squares solutions, symmetric or-thogonal symmetric least-squares solutions, symmetric orthogonal antisymmetricleast-squares solutions and their optimal approximation to the linear matrix equa-tion AX = B, and solve them successfully. 2. For Problem II, we can convert it to another problem of finding the least-squares solutions with the least norm of a new consistent matrix equation. Onthe base of the solutions of Problem I we can apply the iterative method to get

本文所构造的迭代法的优点在于先利用法方程变换将求矩阵方程的最小二乘解转化为求一个相容矩阵方程的解的问题，再利用迭代法对于任意给定的初始矩阵进行迭代，均可在有限步内迭代出所求问题的一个解；可将问题II转化为求新方程的极小范数解的问题，同样用迭代法求解，从而系统且全面地解决了问题I、II在约束矩阵类如中心对称、中心反对称、自反矩阵、反自反矩阵、双对称、对称次反对称、对称正交对称、对称正交反对称矩阵中的最小二乘解及其最佳逼近问题。

If the pattern has a low rate of convergence, the time of the human and machines will be wasted and the answer are not surely attainable.So,we must look for the patterns with the high rate of convergence or try to settle some parameters of the iteration patterns (for instance the overrelaxation parameter of SOR iterative method).

本文第二章针对AOR迭代法考察了当线性方程组的系数矩阵A为(1，1)相容次序矩阵且其Jacobi特征值为纯虚数或零时的迭代收敛范围，最优参数(即最优松弛因子和最优加速因子)及与之相应的谱半径，并将此最优谱半径与相应的SOR的进行比较，定量的给出在不同条件下，AOR和SOR迭代法各有其优越性，从而圆满的解决了在这两种迭代法之间如何适当的选择最佳迭代法的问题。

Simultaneously, the exports of ionization rate and nonionzed concentration are set up as a powerful tool for studying thoroughly the freeze-out effect. dN〓/dp and dN〓/dn are neglected in the linearized equation system of the iteration methods of Newton and Gummel, due to having lower 15 orders or more than dN〓/dn and dN〓/dp, thus the computing effort is cut down with no effect on precision. A new cut-off technique is adopted to accelerate the convergence speed, about twice reduced for Newton iteration method and six times or so for Gummel iteration method. The approximate formulae of Fermi-Dirac statistics are also put forward with simpler form and higher precision. 3. A term dependent on time is added to the electron and hole current succession equations respectively. It is only this model that conservation of charge in transient analysis and alternating small-signal analysis at low temperature can be kept by. 4. The performance of SE-PISCES is explained by the simulation example of PISCES-2B, diode.

研究了低温半导体器件模拟的数值方法：对载流子浓度进行了新的归一化；编制了不考虑掺杂所引进的内建电场时的电离率计算程序；由于低温杂质电离率随偏压状态而变化，为此编制了每次求解迭代时的电离浓度计算程序，并将其插入到求解迭代程序中；同时，设置了杂质电离率和未电离杂质浓度的出口点，为更深入地研究冻析效应提供了有力工具；在Newton迭代法和Gummel迭代法的线性化方程组中忽略了dN〓/dp、dN〓/dn，是因为它们比dN〓/dn、dN〓/dp低15个数量级以上，这样减小了计算量又不影响模拟精度；对Newton迭代法和Gummel迭代法采取了新的截断技术，提高了收敛速度，Newton法迭代法和两次左右，Gummel法减少六次左右；给出了表达式更简单而精度更高的Fermi-Dirac积分近似计算公式。

The downward continuations are made by the iteration method and the FFT for a model and practical data, respectively. The effect of the iteration method is much better than the FFT.

本文用迭代法对模型数据和实际数据进行向下延拓，对比了迭代法与常规的FFT法在位场向下延拓中的效果，迭代法显著优于FFT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。