Fast Laplace Transform Methods for Free-Boundary Problems of Fractional Diffusion Equations

In this paper we develop a fast Laplace transform method for solving a class of free-boundary fractional diffusion equations arising in the American option pricing. Instead of using the time-stepping methods, we develop the Laplace transform methods for solving the free-boundary fractional diffusion equations. By approximating the free boundary, the Laplace transform is taken on a fixed space region to replace discretizing the temporal variable. The hyperbola contour integral method is exploited to restore the option values. Meanwhile, the coefficient matrix has theoretically proven to be sectorial. Therefore, the highly accurate approximation by the fast Laplace transform method is guaranteed. The numerical results confirm that the proposed method outperforms the full finite difference methods in regard to the accuracy and complexity.     

Comparing the Energy of Convergence of One-Step and Two-Step Iterative Methods

The paper establishes the exact error energy compression ratio on each step of the two-step method, which shows a better convergence rate compared with the one-step method with optimal parameter.     

分形图像插值加速收敛方法的改进

图像插值是对数字图像进行不同比例放大过程中必须解决的关键问题。由于分形具有无穷的 细节,采用分形的方法对图像进行插值可以使图像放大后保持较高的视觉分辨率。针对分形图像插 值速度较慢的特点,提出了两种加速收敛的方法,即根据控制学中的有关理论,提出了一种简单易 行的带比较环节的迭代方法,提高迭代收敛速度;此外,尝试一种交叉迭代法,同样达到了加速收敛 的目的。最后,对两种加速方法的实验结果所反映的特点和不足进行了分析和讨论。     

图像插值迭代类算法中加速收敛方法的改进

首先分析了传统松驰参数加速收敛方法的局限性,最后根据控制学中的有关理论,提出了一种简单易行的带比较环节的积分器,使迭代收敛速度大为提高。     

迭代学习控制系统的鲁棒收敛性分析(英)

本文提出一种开闭环配合的滤波器型选代学习控制算法，并将这种算法应用于一般非线性动态系统的轨迹跟踪．对于渐近重复初始条件和渐近周期干扰的情形，通过控制误差估计和输出误差估计，文中分别证明了学习过程的一致收敛性．证明中未采用线性化手段．     

Convergence Analysis and Quality Criteria for an Iterative Schematization of Networks

Schematic networks are linear abstractions of functional networks, such as route networks. Lines in the original network are modified in order to produce a schematic network which satisfies a set of constraints chosen to design the network. A method is described which accomplishes this line transformation using an iterative improvement technique driven by design constraints. The method maintains topological characteristics of the network by the use of simple geometric operations and tests. The iterative process can be repeated until the line displacements become small enough or until it meets user defined stopping criteria. Experimental results are provided to examine the acceptability of outcomes and the convergence of the applied iterative technique. Criteria for measuring the quality of results, as well as for stopping the iterative approach are presented.

On a System of Adaptive Coupled PDEs for Image Restoration

In this paper, we consider a coupled system of partial differential equations (PDEs) based model for image restoration. Both the image and the edge variables are incorporated by coupling them into two different PDEs. It is shown that the initial-boundary value problem has global in time dissipative solutions (in a sense going back to P.-L. Lions), and several properties of these solutions are established. Some numerical examples are given to highlight the denoising nature of the proposed model along with some comparison results.     

Analysis of Iterative Methods for Solving a Ginzburg-Landau Equation

Very recently we have proposed to use a complex Ginzburg-Landau equation for high contrast inpainting, to restore higher dimensional (volumetric) data (which has applications in frame interpolation), improving sparsely sampled data and to fill in fragmentary surfaces. In this paper we review digital inpainting algorithms and compare their performance with a Ginzburg-Landau inpainting model. For the solution of the Ginzburg-Landau equation we compare the performance of several numerical algorithms. A stability and convergence analysis is given and the consequences for applications to digital inpainting are discussed.First online version published in June, 2005     

迭代方法中基于渐近规模的通信与计算比分析

迭代方法是科学计算中求解大规模稀疏线性代数方程组最常用的方法.大量实际应用表明,迭代方法通常具有较高的通信与计算比,只有在粗粒度并行下才能取得较好的并行可扩展性能.而实际应用大规模计算的需求和当前多核/众核体系结构的发展趋势要求迭代方法具备细粒度并行可扩展能力.文中引入渐近规模,即满足加速条件的计算规模下界,来反映并行迭代方法适应细粒度并行的能力,并由此刻画通信与计算比.基于矩阵的稀疏模式及其通信模式、机器的通信参数和迭代方法的基本运算,给出了渐近规模的理论预测公式.在一台包含128个双路4核计算节点的并行机上,分别基于纯进程并行(MPI)和进程/线程混合并行(MPI/OpenMP),以实际应用中3种常用迭代方法Jacobi、CG、BiCGSTAB为例,分析其渐近规模.并行可扩展性测试表明了渐近规模用于刻画迭代方法通信与计算比的准确性.对于纯进程情形,给出了渐近规模的理论预测与实际测试的对比,表明了理论预测结果的正确性.最后,基于这些结果,从迭代方法的算法设计和并行实现等方面讨论了面向未来更大规模的计算系统,降低通信与计算比的途径.     

基于Laplace变换的空时分组编码误符号率性能分析

分析了空间相关Rayleigh衰落信道下采用空时分组编码的MIMO通信系统的误符号率.利用Laplace变换推导了空时分组编码系统在接收端信噪比的概率密度函数,得出了由基本初等函数表示的线性调制下空时分组编码系统误符号率的闭合表达式.仿真结果证明了性能分析的有效性.     

非线性工业过程控制系统的迭代学习控制与收敛性分析

基于工业过程稳态优化中递阶控制结构和线性工业过程控制系统中的迭代学习控制规律, 本文对饱和非线性工业过程控制系统和变增益非线性工业过程控制系统施行迭代学习控制, 分别给出加权PD 型闭环迭代学习控制算法和加权幂型开闭环迭代学习控制算法, 提出了期望目标轨线的 δ 可达性和迭代学习算法的ε 收敛性的概念. 利用Bellman Gronwall不等式和λ 范数理论, 论证了算法的收敛性. 数字仿真表明, 迭代学习控制能有效改善非线性工业控制系统在稳态优化时的动态品质.     

Turbo码译码的收敛性与停止迭代判据

为减少译码延时,根据Turbo码的似然比的可靠性讨论了Turbo的收敛性,提出了两种基于可靠性的迭代停止判决,通过仿真译码时的平均迭代次数明显减少,并且所获得的性能几乎没有下降,表明提出的迭代停止判据有效。     

Convergence Analysis of Wireless Remote Iterative Learning Control Systems with Channel Noise

Channel noise, including sensor‐to‐controller(SC) noise and controller‐to‐actuator(CA) noise, impacts the convergence of wireless remote iterative learning control (ILC) system significantly. In this paper, the relationship between output error, SC noise and CA noise is obtained firstly by super‐vector formulation, and then the norm of output error vector covariance matrix is employed to analyze the convergence of the system in presence of SC noise and CA noise. Upper bound of the norm at any sample time reveals that the SC noise is accumulated only in iteration domain, while the CA noise is accumulated not only in iteration domain but also in time domain. Furthermore, the accumulated effect of the CA noise in time domain is ruled by system matrices, so the values of which determine the effect of the CA noise is greater or less than that of the SC noise on convergence of the system. Finally, some simulation results are given to illustrate correctness of the result.     

Convergence Analysis of Spectral Galerkin Methods for Volterra Type Integral Equations

This work is to provide spectral and pseudo-spectral Jacobi-Galerkin approaches for the second kind Volterra integral equation. The Gauss-Legendre quadrature formula is used to approximate the integral operator and the inner product based on the Jacobi weight is implemented in the weak formulation in the numerical implementation. For some spectral and pseudo-spectral Jacobi-Galerkin methods, a rigorous error analysis in both the infinity and weighted norms is given provided that both the kernel function and the source function are sufficiently smooth. Numerical experiments validate the theoretical prediction.     

Arnold变换三种恢复方法的比较分析

为了提高Arnold变换图像加密或Arnold变换图像水印算法的执行效率,对Arnold变换的三种恢复方法进行效率分析.以256×256的灰度图像加密为例,对其进行仿真研究.分析三种恢复方法与迭代次数、变换周期的关系,从而得出三种恢复方法的适用场合.这一研究结果将有助于Arnold变换在信息安全方面的应用研究.     

AzureOP:基于Windows Azure云并行计算的期权定价SaaS

计算速度对于期权交易者至关重要,关系到如何有效地制定价格并评估相应的风险,而云并行计算提供的随收随付制（Pay-as-You-Go）可以实现低成本运行。在微软云平台Windows Azure的基础上,开发了基于云并行计算的期权定价试点云软件AzureOP,该软件以较低的费用提供了低风险和高速度,并给出了AzureOP对于美式期权价格的模拟结果,绘制了对应的期权价格定价曲线和定价曲面。最后,对云并行计算在金融应用上的优势和不足进行了总结和讨论,同时举例说明了试点云软件AzureOP的具体细节。     

Radial Basis Function Methods for the Rosenau Equation and Other Higher Order PDEs

Meshfree methods based on radial basis function (RBF) approximation are of interest for numerical solution of partial differential equations because they are flexible with respect to the geometry of the computational domain, they can provide high order convergence, they are not more complicated for problems with many space dimensions and they allow for local refinement. The aim of this paper is to show that the solution of the Rosenau equation, as an example of an initial-boundary value problem with multiple boundary conditions, can be implemented using RBF approximation methods. We extend the fictitious point method and the resampling method to work in combination with an RBF collocation method. Both approaches are implemented in one and two space dimensions. The accuracy of the RBF fictitious point method is analyzed partly theoretically and partly numerically. The error estimates indicate that a high order of convergence can be achieved for the Rosenau equation. The numerical experiments show that both methods perform well. In the one-dimensional case, the accuracy of the RBF approaches is compared with that of the corresponding pseudospectral methods, showing similar or slightly better accuracy for the RBF methods. In the two-dimensional case, the Rosenau problem is solved both in a square domain and in an irregular domain with smooth boundary, to illustrate the capability of the RBF-based methods to handle irregular geometries.     

Turbo—CPM系统迭代检测收敛性的研究

根据连续相位调制(CPM)的分解模型,CPM调制可以分解为连续相位编码(CPE)和无记忆调制(MM),基于CPE的记忆和递归特性,结合外部的Turbo码及交织器,建它了Turbo-CPM系统模型.针对短帧系统在迭代检测过程中存在的正反馈现象,设计了一种基于加权外信息交换的迭代检测接收机.理论分析与仿真结果表明:在低信噪比条件下,所设计的接收机不仅能够有效地抑制系统中存在的正反馈现象,改善系统的收敛性,提高系统的误比特率性能,而且减少了平均迭代次数,提高了系统的实时性.