Speeding up the FMMR perfect sampling algorithm: A case study revisited

In a previous paper by the second author, two Markov chain Monte Carlo perfect sampling algorithms—one called coupling from the past (CFTP) and the other (FMMR) based on rejection sampling—are compared using as a case study the move‐to‐front (MTF) self‐organizing list chain. Here we revisit that case study and, in particular, exploit the dependence of FMMR on the user‐chosen initial state. We give a stochastic monotonicity result for the running time of FMMR applied to MTF and thus identify the initial state that gives the stochastically smallest running time; by contrast, the initial state used in the previous study gives the stochastically largest running time. By changing from worst choice to best choice of initial state we achieve remarkable speedup of FMMR for MTF; for example, we reduce the running time (as measured in Markov chain steps) from exponential in the length n of the list nearly down to n when the items in the list are requested according to a geometric distribution. For this same example, the running time for CFTP grows exponentially in n. © 2003 Wiley Periodicals, Inc. Random Struct. Alg., 2003     

Global linear convergence of a path-following algorithm for some monotone variational inequality problems

We consider a primal-scaling path-following algorithm for solving a certain class of monotone variational inequality problems. Included in this class are the convex separable programs considered by Monteiro and Adler and the monotone linear complementarity problem. This algorithm can start from any interior solution and attain a global linear rate of convergence with a convergence ratio of 1 ?c/√m, wherem denotes the dimension of the problem andc is a certain constant. One can also introduce a line search strategy to accelerate the convergence of this algorithm.     

Unconstrained and constrained global optimization of polynomial functions in one variable

In Floudas and Visweswaran (1990), a new global optimization algorithm (GOP) was proposed for solving constrained nonconvex problems involving quadratic and polynomial functions in the objective function and/or constraints. In this paper, the application of this algorithm to the special case of polynomial functions of one variable is discussed. The special nature of polynomial functions enables considerable simplification of the GOP algorithm. The primal problem is shown to reduce to a simple function evaluation, while the relaxed dual problem is equivalent to the simultaneous solution of two linear equations in two variables. In addition, the one-to-one correspondence between the x and y variables in the problem enables the iterative improvement of the bounds used in the relaxed dual problem. The simplified approach is illustrated through a simple example that shows the significant improvement in the underestimating function obtained from the application of the modified algorithm. The application of the algorithm to several unconstrained and constrained polynomial function problems is demonstrated.     

基于L~1度量分析的图象分解与重构算法

Mallat‘s decompositon and reconstruction algorithms are very important in the the field of wavelet theory and its applications to signal processing.Wavelet Anal-ysis,which is based on L^2(R) space,can eliminate redundancy of signals with the help of orthogonality and characterize the processing precision with the meansquare error.In the recent years,it is understood that the mean square measuredoes not match human visual sensitivity well.From the point of view,R.DeVore studied L^1 measure instead.Similarly,considering the principles of image com-pression,Yang introduced and dealt with orthogonality in L^1 space based on thebest approximation theory,and consequently established the corresponding decom-position and reconstruction algorithms for signals.In this paper,error analyses for the algorithms above are taken and the selection of the best parameters in the algorithms are discussed in detail.Finally,the algorithms are compared with the classical Haar and Daubechies‘‘s orthogonal wavelets based on the singal-to-noiseratio data computed.     

AN ALGORITHM FOR JORDAN CANONICAL FORM OF A QUATERNION MATRIX

In this paper, we first introduce a concept of companion vector, and study the Jordan canonical forms of quaternion matrices by using the methods of complex rep resentation and companion vector, not only give out a practical algorithm for Jordan canonical form J of a quaternion matrix A, but also provide a practical algorithm for corresponding nonsingular matrix P with P-1AP = J.     

Multivariate Refinement Equations and Convergence of Cascade Algorithms in Lp（0〈p〈1）Spaces

We consider the solutions of refinement equations written in the form

二维刚性边值问题的小波-吉尔解法

本文利用微分方程数值解的离散小波表示，讨论了此类方程在满足一定初始条件和边值条件下，在一个方向上利用小波伽辽金法，另一方向上利用吉尔方法进行求解，提出了一种解二维刚性初，边值问题的小波数值算法，计算结果表明，利用该方法所求得的数值解精度高，而且由小波特有的性质，它特别适用于求解带有奇异摄动的刚性问题。     

平行机半在线排序问题研究(Ⅰ)

对半在线平行机排序问题的研究进展作了详细综述和进一步探讨。文章给出半在线排序问题的背景、定义、分类和求解。介绍它们定义和在不同机器环境和目标函数下半在线排序问题分类，以及第一类半在线模型的近似算法的设计及其竞争比分析。     

空间有理参数多项式曲线的整数级绘制算法

讨论了空间有理曲线中心投影后导数上界的估计，基于曲线各阶差分的递推计算，给出了空间有理参数多项式曲线的快速绘制算法．算法只用到整数的加减法，效率高．     

A kind of distortion of mean velocity profile in pipe Poiseuille flow and its stability behaviour

This paper presents a kind of distortion of Hagen-Poiseuille velocity profile in pipe Poiseuille flow. This distortion can be regarded as a general expression of the influence on the mean flow by nonlinear interaction of various components of axisymmetric perturbations. Through the investigation of the stability behaviour of this velocity profile, this paper obtains unstable result induced by axisymmetric perturbations for the first time, and thus presents a new possible approach which leads to instability of Hagen-Poiseuille flow.