An alternating projected gradient algorithm for nonnegative matrix factorization

Due to the extensive applications of nonnegative matrix factorizations (NMFs) of nonnegative matrices, such as in image processing, text mining, spectral data analysis, speech processing, etc., algorithms for NMF have been studied for years. In this paper, we propose a new algorithm for NMF, which is based on an alternating projected gradient (APG) approach. In particular, no zero entries appear in denominators in our algorithm which implies no breakdown occurs, and even if some zero entries appear in numerators new updates can always be improved in our algorithm. It is shown that the effect of our algorithm is better than that of Lee and Seung’s algorithm when we do numerical experiments on two known facial databases and one iris database.     

The Index of the Complex Eigenvalues of a Parity Progressive Population Operator

In this paper we discuss the index of the complex eigenvalue of a parity progressive population operator. Under certain conditions, we first prove that all the complex eigenvalues of this operator, except at most finitely many ones, are of index 1, and then, as an application of this result, we obtain the asymptotic expansion of the solution of the corresponding parity progressive population equation.     

THE INVERSE EIGENPROBLEM WITH RANK-ONE UPDATING AND ITS STABLITY

Let ∑, Г be two n-by-n diagonal matrices with σi,γi as their diagonals. For the inverse eigenvalue problem: look for y∈Rn such that Г + yyT is similar to ∑, we prove thatu also the sufficient condition for the solvability of this inverse problem. Its solution (set) is given explicitly. In some case, the problem is unstable. But we prove that the sums of the square of some contigious components keep stable, i.e., small sum keeps small, large sum has a small relative perturbation, see Theorem 3.     

逐步增加Ⅱ型截尾下指数分布恒加试验的统计分析

本文对逐步增加Ⅱ型截尾下指数分布场合恒定应力加速寿命试验进行了统计分析,得到参数的最大似然估计存在唯一的充要条件。最后通过模拟例子表明最大似然估计是有效的。     

基于对偶性原理捷联惯导划船误差补偿优化算法

先介绍了算法的对偶性原理，并根据此原理和圆锥误差补偿的一般形式，得到了陀螺和加速度计任意子样数下划船误差补偿的一般形式；然后在经典的划船运动条件下，对划船误差补偿算法的系数进行优化，得到了优化后的通用公式及其算法漂移；最后，通过对圆锥误差算法和划船误差算法的复杂度、算法漂移的比较，得出一些有益结论。基于该方法可以充分利用圆锥误差算法的已有结果，由计算机编程计算得到划船误差补偿的任意子样数算法，无需繁琐的重复性推导。     

常微分方程解的存在唯一性定理教学研究

探讨了常微分方程初值问题解的存在唯一性定理教学策略.为便于教学和有利于学生理解并掌握其思想方法,对定理证明过程的表述作了命题化处理,给出了Picard逐步逼近法的应用实例,提出了教学讨论与知识拓展的一些有益内容.