高收敛率的Rayleigh商型迭代格式

本文提出一些高收敛率的Ｒａｙｌｅｉｇｈ商型迭代格式，用以求解矩阵特征值问题ＡＸ＝λＸ，Ａ∈Ｃｎｘｎ。对于正规矩阵Ａ，本文的ｌ级ＨＲＱＩ法具有２ｌ＋１阶局部敛率。著名的ＲＱＩ法就是１级ＨＲＱＩ法。在时，如用Ｇａｕｓｓ消元法解有关的线性方程组，则ｌ级ＨＲＱＩ格式在每个迭代步中的计算量与ＲＱＩ的计算量基本持平。对非正规矩阵，与著名的Ｏｓｔｒｏｗｓｋｉ双边迭代法（ＯＴ）相对应，本文提出Ｉ级ＨＯＴＩ迭代格式。ｌ级ＨＯＴＩ用于非亏损矩阵时，具有２ｌ＋１阶局部效率。而ＯＴＩ就是１级ＨＯＴＩ法。同样，ｌ级ＨＯＴＩ与ＯＴＩ的每步迭代的计算量基本持平。

高收敛率的GRQI型迭代法

对广义特征值问题Ａｘ＝λＢｘ，Ａ，Ｂ∈Ｃｎ×ｎ（１），本文提出ｌ级ＨＧＲＱＩ格式，其中ｌ为任一自然数，它的局部收敛阶为ｌ＋１。当ｌ＝１时，它就是文［１］中所述的ＧＲＱＩ格式，如果用Ｇａｕｓｓ消元法解有关线性方程组，则当１＜ｌ＜＜ｎ时，ｌ级ＨＧＲＱＩ在每个迭代步中的运算量与ＧＲＱＩ的运算量基本持平。本文又将适用于普通特征值问题Ａｘ＝λｘ的Ｏｓｔｒｏｗｓｋｉ双边送代法（ＯＴＩ）推广到ｌ级ＨＧＯＴＩ，它适用于问题（１），且具有局部收敛率ｌ十１。当ｌ＝１且（１）中的Ｂ＝Ｉ时，ＨＧＯＴＩ便成了ＯＴＩ。ＨＧＯＴＩ与ＨＧＲＱＩ有类似的优点。

一个高精度收敛的变系数微分方程精确解析法

文[1]给出精确解析法,可用于求解任意变系数微分方程,所得到的解具有二阶收敛精度.在此基础上,本文以变截面梁弯曲为例,给出一个高精度的算法.不增加工作量的情况下可达到四阶收敛精度.具有计算快,简单等特点,文末给出算例,仅用很少的单元即可获得高的收敛精度,表明了本文理论的正确性.

“放管服”改革和“互联网+”背景下高校财务网络安全问题的思考

2018年8月,国务院印发了《全国深化“放管服”改革转变政府职能电视电话会议重点任务分工方案》。随着高校财务系统“放管服”政策改革,互联网的开放性和安全漏洞带来的风险无处不在。本文旨在深化改革后,探索高校财务管理网络进行高安全性和便捷性的网络架构,以实现兼顾“放管服”目标且满足高可用、高收敛、信息可追溯的财务网络安全架构。

基于非线性规划问题GA的Matlab程序

利用Matlab软件强大的编程、计算功能 ,结合遗传控制理论提出了一种基于非线性规划问题遗传算法的Matlab程序 ,并且对遗传算法有所改进。通过多峰函数优化问题的仿真试验 。

Numerical simulation of LWD resistivity response of carbonate formation using self-adaptive hp-FEM

Most of the carbonate formation are highly heterogeneous with cavities of different sizes, which makes the prediction of cavity-filled reservoir in carbonate rocks difficult. Large cavities in carbonate formations pose serious threat to drilling operations. Logging-whiledrilling （LWD） is currently used to accurately identify and evaluate cavities in reservoirs during drilling. In this study, we use the self-adaptive hp-FEM algorithm simulate and calculate the LWD resistivity responses of fracture-cavity reservoir cavities. Compared with the traditional h-FEM method, the self-adaptive hp-FEM algorithm has the characteristics of the self-adaptive mesh refinement and the calculations exponentially converge to highly accurate solutions. Using numerical simulations, we investigated the effect of the cavity size, distance between cavity and borehole, and transmitted frequency on the LWD resistivity response. Based on the results, a method for recognizing cavities is proposed. This research can provide the theoretical basis for the accurate identification and quantitative evaluation of various carbonate reservoirs with cavities encountered in practice.

Adaptive terminal sliding mode control for high-order nonlinear dynamic systems

An adaptive terminal sliding mode control (SMC) technique is proposed to deal with the tracking problem for a class of high-order nonlinear dynamic systems. It is shown that a function augmented sliding hyperplane can be used to develop a new terminal sliding mode for high-order nonlinear systems. A terminal SMC controller based on Lyapunov theory is designed to force the state variables of the closed-loop system to reach and remain on the terminal sliding mode, so that the output tracking error then converges to zero in finite time which can be set arbitrarily. An adaptive mechanism is introduced to estimate the unknown parameters of the upper bounds of system uncertainties. The estimates are then used as controller parameters so that the effects of uncertain dynamics can be eliminated. It is also shown that the stability of the closed-loop system can be guaranteed with the proposed control strategy. The simulation of a numerical example is provided to show the effectiveness of the new method.

EVCP:a convergence time improved high-speed transport congestion control protocol

The Internet evolves to incorporate very-high-bandwidth optical links and more large-delay satellite links. TCP faces new challenges in this unique environment. Theory and experiments showed that TCP becomes inefficient and is prone to be unstable as the per-flow product of bandwidth and latency increases, regardless of the queuing scheme. Variable-structure congestion Control Protocol (VCP) is proposed to address these problems. However, VCP has problem in terms of convergence time, i.e., it takes a long time for a new VCP flow to achieve fair bandwidth allocation if the existing VCP flows have large con- gestion windows. This paper proposed an Extended Variable-structure congestion Control Protocol (EVCP), which adopted a convergence controller. The basic idea of convergence controller is that if a flow has larger window than its fair window, its congestion window should be decreased more aggressively than usual in Multiplicative Decrease (MD) phase. Simulations showed that EVCP has better performance in terms of convergence time while keeping the advantages of VCP.

Approximation and Superconvergence Analysis for a New Higher Order Wilson Element to Sobolev Type Equations

In this paper, a new higher order Wilson element is presented, and the convergence is proved. Then the interpolation postprocessing technique is used to obtain the global superconvergence and posterior error estimate of higher accuracy of this new element for the Sobolev type equations.

Existence of Solutions to a Class of Higher-Order Singular Boundary Value Problem for One-Dimensional p-Laplacian

This paper deals with the existence of positive solutions for the problem {（Фp（x^（n-1）（t）））′＋f（t,x,…,x^（n-1）=0,0〈t〈1, x^（i）（0）=0,0≤i≤n-3, x^（n-2）（0）-B0（x^（n-1）（0））=0,x^（n-2）（1）＋B1（x^（x-1）（1））=0, where Фp（s） = ｜s｜^p-2s, p 〉 1. f may be singular at x^（i） = 0, i = 0,...,n- 2. The proof is based on the Leray-Schauder degree and Vitali＇s convergence theorem.

Convergence of Gaussian Quadrature Formulas for Power Orthogonal Polynomials

In classical theorems on the convergence of Gaussian quadrature formulas for power orthogonal polynomials with respect to a weight w on I （a,b）, a function G E S（w）= （f： fxlf（x）lw（x）dx 〈 ∞ satisfying the conditions G（2J）（x） ：〉 O, x E （a,b）, j = 0, 1 , and growing as fast as possible as x→ a- and x → b-, plays an important role. But to find such a function G is often difficult and complicated. This implies that to prove convergence of Gaussian quadrature formulas, it is enough to find a function G E S（w） with G ≥ 0 satisfying