An efficient numerical method for preconditioned saddle point problems

In this paper, we consider the solution of linear systems of saddle point type by a preconditioned numerical method. We first transform the original linear system into two sub-systems with small size by a preconditioning strategy, then employ the conjugate gradient (CG) method to solve the linear system with a SPD coefficient matrix, and a splitting iteration method to solve the other sub-system, respectively. Numerical experiments show that the new method can achieve faster convergence than several effective preconditioners published in the recent literature in terms of total runtime and iteration steps.     

Root determination by use of Padé approximants

In this paper we describe a new technique for generating iteration formulas — of arbitrary order — for determining a zero (assumed simple) of a functionf, assumed analytic in a region containing the zero. The 1/p Padé Approximant (p0) to the functiong(t)f(z) is formed wherez=w+t, using the Taylor series forf at the pointw, an approxination to the zero off. The value oft for which the 1/p Padé Approximant vanishes provides the basis of iteration formulas of orderp+2.Some known iteration formulas, e.g., Newton-Raphson's, Halley's and Kiss's of order of convergence two, three and four, are directly obtained by settingp=0,1 and 2, respectively.     

一类生产安排优化问题的检验数及最优解的确定

本文是《一类生产安排优化问题的基的特征与基可行解的求法》的续篇。对线性规则问题: 给出了相对应的检验数计算公式: 其中c_i,d_j是议程组(u_1…,u_m,V_1,…,V_n)B=C_B的解。并给出了调整负检验数的方法,从而使这一类线性规划问题得到较简单的单纯形解法。     

一类复Schrdinger方程和实Klein-Gordon方程耦合方程组解的整体存在性

本文主要对下面一类复非线性Schrodinger方程和实非线性Klein-Gordon方程的耦合方程组(1)研究其解的整体存在性和渐近性态,这里f,g满足|f(λ)|,|g(λ)|=O(|λ|~(α 1)) 在λ=0附近(2)其中λ=(λ_0,λ_1……λ_(n 1),λ_(n 2)),α是≥1的整数。我们在适当的光滑性的假定下,证明了当n>2α 2/α~2时,问题(1)对“小”初值存在唯一的整体光滑解u,v,且当t→ ∞时,u,v具有衰减性质||u(t)||_L~(2α 2)=O(t~(-απ/2α 2),||v(t)||_L~(2α 2)=O(t~(-απ/2α 2)。     

直射线CT技术的局限性

分析了利用弯曲路径旅行时进行直射线反演的若干结果,对直射线CT技术的局限性进行了讨论.研究认为,对所讨论的区域而言,若介质速率的相对变化较大时,运用反演的结果不能很好地确定区域的内部结构;而当介质速率的相对变化较小时,对5m左右的薄层,它亦只能确定速度异常区的存在,而不能很好地确定其速度异常的数值.     

用有限元迭代法分析有滚柱支架的架空热力管道系统

当架空热力管道系统中有滚柱支架时,热胀的管道与支架问的横向和轴向位移的摩擦系数不同,导致摩擦接触面处于正交各向异性摩擦接触状态.本文提出了处理这种摩擦接触情况的基本思想和分析方法,用有限元迭代法分析计算了有滚柱支架的架空热力管道系统的位移和应力.计算结果表明,影响管线变形的主要因素是沿管道横向的摩擦力.设置滚柱支架使管线在支架处的横向位移为滚动,可以减小摩擦对位移的影响.     

具有可变几何喷嘴的增压器轴流涡轮热力计算方法

本文提出具有可变几何喷嘴的增压器轴流涡轮热力计算方法。引入三个脉冲系数将脉冲涡轮按等压涡轮计算。给定通流部分尺寸,利用可变几何喷嘴来满足所驱动压气机和涡轮的配合。考虑各部实际损失,采用吴仲华燃气热力性质表迭代计算求出反动度、喷嘴出气角和喉口面积。可给定废气初温时迭代所需的初压或给定初压时迭代所需的初温,并算出涡轮当量通流面积。计算结果表明迭代计算是收敛的,算出的喷嘴喉口面积与实际相符。     

The parallel calculation of the ground-state correlation energy of Helium atom

When we use Modified Configuration Interaction method (MCI) to calculate the correlation energy of double-electron systems, for obtaining the higher precision, we always need huge calculations. In order to handle this problem, which will cost much CPU time and memory room if only using a single computer to do it, we now adopt the parallel multisection recurrence algorithm. Thus we can use several CPUs to get the ground-state energy of a Helium atom at the same time. Supported by Opening Foundation of Laboratory of Wavy Spectrum and Atomic and Molecular Physics, Wuhan Institute of Physics, Chinese Academy of Sciences Liu Lianjun: born in 1946, Associate professor     

一种新的多维非线性模拟电路频域分析方法——算子广义幂级数分析法

本文叙述一种将牛顿法、部分牛顿法和割线迭代法融合为能分析多维非线性模拟电路,且具有更强的收敛性能的算法.本方法适合于非线性模拟电路的分析,可直接处理频域中的二维非线性元件.文中用测量单音和双音激励一个MESFET放大器的例子所证实.     

代换序列的部分和研究（Ⅰ）

设σ为集合A={1,-1}上的代换,x=x_1,…x_n…∈(1,-1}~N为σ的不动点,s(N)=sum from j=1 to N(x_j)为x的前N项的和.本文首先确定σ的第n次迭代σ~n(1)的部分和的极大值与极小值。然后利用这些结果完全确定了s(N)的渐近性质。