Nonmonotone Inexact Newton Method for the Extended Linear Complementarity Problem

This paper presents a nonmonotone inexact Newton-type method for the extended linear complementarity problem (ELCP). We first reformulate the optimization system of the ELCP problem into a system of smoothed equations. Then we solve this system by a nonmonotone inexact Newton-type algorithm. The global convergence is obtained and numerical tests for some classes of ELCP include linear complementarity, horizontal linear complementarity, and generalized linear complementarity problems are also given to show the e?ciency of the proposed algorithm.     

基于梯度与曲率相结合的图像平滑模型的研究

在图像处理过程中, 为了在图像去噪时更好地保留图像边缘细节信息, 首先结合扩散系数和曲率的性质建立了一个曲率平滑模型. 考虑到图像受到噪声污染时曲率会发生显著变化, 将图像的水平集曲率作为一个检测因子代入到上述模型中, 提出了一个梯度与曲率相结合的新模型. 分析与仿真结果表明, 该模型与Perona-Malik模型相比较保留了更多的图像信息, 有效地增强了图像尖锐的边缘, 同时很好地保持了图像的直线和曲线边缘、角点、斜坡和小尺度特征, 是一个理想的模型.     

Weighted Sobolev L2 estimates for a class of Fourier integral operators

In this paper we develop elements of the global calculus of Fourier integral operators in ${{\mathbb R}^n}$ under minimal decay assumptions on phases and amplitudes. We also establish global weighted Sobolev L² estimates for a class of Fourier integral operators that appears in the analysis of global smoothing problems for dispersive partial differential equations. As an application, we exhibit a new type of weighted estimates for hyperbolic equations, where the decay of data in space is quantitatively translated into the time decay of solutions.     

A new one‐step smoothing newton method for the second‐order cone complementarity problem

In this paper, we present a new one‐step smoothing Newton method for solving the second‐order cone complementarity problem (SOCCP). Based on a new smoothing function, the SOCCP is approximated by a family of parameterized smooth equations. At each iteration, the proposed algorithm only need to solve one system of linear equations and perform only one Armijo‐type line search. The algorithm is proved to be convergent globally and superlinearly without requiring strict complementarity at the SOCCP solution. Moreover, the algorithm has locally quadratic convergence under mild conditions. Numerical experiments demonstrate the feasibility and efficiency of the new algorithm. Copyright © 2010 John Wiley & Sons, Ltd.     

非线性不等式组的光滑近似方法及其收敛性

将非线性不等式组的求解转化成非线性最小二乘问题,利用引入的光滑辅助函数,构造新的极小化问题来逐次逼近最小二乘问题.在一定的条件下,文中所提出的光滑高斯-牛顿算法的全局收敛性得到保证.适当条件下,算法的局部二阶收敛性得到了证明.文后的数值试验表明本文算法有效.     

基于一个新的NCP函数的光滑牛顿法求解非线性互补问题

本文研究了非线性互补的光滑化问题.利用一个新的光滑NCP函数将非线性互补问题转化为等价的光滑方程组,并在此基础上建立了求解P0-函数非线性互补问题的一个完全光滑化牛顿法,获得了算法的全局收敛性和局部二次收敛性的结果.并给出数值实验验证了理论分析的正确性.     

控制点优化磨光算法在长江径流量预测中的应用

盈亏修正磨光法所得到的逼近效果仍然很差,通过控制点的参数优化和目标函数的最小,提出一种控制点优化磨光算法,利用这个算法得到参数后代入模型,使预测的精度得到提高.通过实例,该算法简单易行,并通过相对误差进行了分析,控制点优化磨光算法所得到的预测值好于神经网络模型、PPAR和小波网络模型的预测值,这为研究磨光法提供了较好的分析方法.     

Interactive effects of local smoothing window size and fundamental frequency on shimmer calculation

Slow amplitude modulation of human voice was approximated by a sinusoidal wave. The theoretical effects of smoothing window size, F₀, and modulation frequency on window amplitude average as well as calculated shimmer were mathematically derived. Subsequently, the theoretical predictions were tested using idealized and real voice signals from normal speakers. The theoretical and experimental results suggest that shimmer (when calculated using a smoothing window) is a function of window duration and modulation frequency. Window duration when defined as a constant number of pitch periods varies from speaker to speaker depending on their F₀. It may not be desirable to use local smoothing windows with a constant number of cycles for shimmer computation, especially if voices with known low-frequency amplitude modulations but notably different fundamental frequencies are compared.     

On λ[S] Semigroup of Semigroup

Wehaveintroducedσconstructionofrings[1],[2]withhomomorphismofmodulesofringsinringtheoryanddiscussedsomerelationsbetweenringRand[R]σandRσ.Thecongruencesandidealsareequevalent,sohomomorphismsandidealsarecorrespondingonebyoneinringtheory;buthomomorphismsandidealsarenotequevalentinsemigrouptheory,homomor-phismsandcongreuncesarecorrespondingonebyone,thekernerofhomomorphismsisacon-greunces,hencethediscussionofsimilarproblemsinringtheoryandsemigrouptheoryhasgreatdifference.Firstweintroducethenoti…     

<Emphasis Type="Italic">m</Emphasis>-Dissipativity of Kolmogorov Operators Corresponding to Burgers Equations with Space-time White Noise

In this article, we prove new a priori estimates on the solutions of the Burgers equation driven by a space-time white noise and on the associated invariant measure. We also prove smoothing properties for the transition semi-group. This is obtained thanks to the introduction of a modified Kolmogorov operator. These results are then used to prove that the Kolmogorov operator associated to the Burgers equation is m-dissipative. This implies several properties on the Kolmogorov equation.