用二值矩阵表示研究格矩阵的{1}-广义逆和{1,2}-广义逆

用二值矩阵表示的方法(即将格矩阵表示成二值矩阵的线性组合)研究了分配格上矩阵的{1}-广义逆和{1,2}-广义逆. 讨论了{1}-广义逆和{1,2}-广义逆存在的充分必要条件. 给出了判断这些逆是否存在且存在时找出所有这些逆的算法. 从而解决了Kim和Roush(K.H.Kim,F.W.Roush. Generalized fuzzy matrix. Fuzzy Sets and Systems,1980,4(3):293～315)及部分解决了Cao和Kim(Z.Q.Cao,K.H.Kim,F.W.Roush. Incline algebra and applications. New York:John Wiley,1984)提出的问题.     

利用分片贪婪算法求解分片稀疏恢复问题

在实际应用中,有一些信号是具有分片的结构的.本文我们提出一种分片正交匹配追踪算法(P\_OMP)来求解分片稀疏恢复问题,旨在保护分片信号中的分片结构(或者小尺度非零元).P\_OMP算法是基于CoSaMP和OMMP算法的思想上延伸出的一种针对分片稀疏问题的贪婪算法. P\_OMP算法不仅仅具有OMP算法的优势,还能够在比CoSaMP方法更松弛的条件下得到同样的误差下降速率.进一步,P\_OMP~算法在保护分片稀疏信号的尺度细节信息上表现的更好.数值实验表明相比于CoSaMP, OMP, OMMP和BP算法, P\_OMP算法在分片稀疏恢复上更有效更稳定.     

局部环上幂等矩阵线性组合广义逆之间的关系

设R是2为单位的局部环.研究了R上三个两两可换的n阶非零幂等矩阵的线性组合广义逆之间的包含关系,确定了R上一类特殊矩阵广义逆的列表算法.利用这种列表算法和相关的矩阵理论,得到了这些矩阵线性组合广义逆之间的包含关系的充要条件,推广了矩阵自反广义逆的逆反律的相关结果.     

用随机奇异值分解算法求解矩阵恢复问题

本文研究了大型低秩矩阵恢复问题.利用随机奇异值分解（RSVD）算法,对稀疏矩阵做奇异值分解.该算法与Lanczos方法相比,在误差精度一致的同时运算时间大大降低,且该算法对相对低秩矩阵也有效.     

布尔矩阵的Cline逆

研究了布尔矩阵的广义逆,首先引入了布尔矩阵的Drazin逆及Cline逆,利用布尔矩阵的性质证明了任意布尔矩阵均有Drazin逆,从而证得任意布尔矩阵均有Cline逆,且Cline唯一.而且,在A+存在的情况下Ac=A+.最后证明了Cline逆的一些性质.     

用随机奇异值分解算法求解矩阵恢复问题（英文）

本文研究了大型低秩矩阵恢复问题.利用随机奇异值分解(RSVD)算法,对稀疏矩阵做奇异值分解.该算法与Lanczos方法相比,在误差精度一致的同时运算时间大大降低,且该算法对相对低秩矩阵也有效.     

基于多模型自适应估计的姿态敏感器误差校准

提出一种基于多模型自适应估计(MMAE)的星敏感器低频误差(LFE)校准方法.星敏感器低频误差主要是由空间热环境的周期性变化造成的,会对卫星姿态确定精度造成显著影响.低频误差的影响可以通过扩维卡尔曼滤波(AKF)进行校准.但是,在星敏感器观测量中不存在低频误差的情况下,AKF的姿态估计精度往往不及传统卡尔曼滤波(KF).针对这一问题,将KF与AKF相结合,设计了基于MMAE的姿态确定滤波算法,该算法能够根据星敏感器在轨误差特性自适应的选择KF或AKF算法进行滤波.仿真结果表明,所提算法综合性能优于KF和AKF,适用于对姿态确定精度要求较高的高分辨率对地观测卫星.     

关于布尔矩阵的广义Moore-Penrose逆

讨论布尔矩阵的广义Moore-Penrose逆.给出了一些广义Moore-Penrose逆存在的充要条件以及广义Moore-Penrose逆的一些刻划.     

Banach空间中线性算子的齐性广义逆

本文首先在Banach空间内引进拟线性投影算子的概念,由此给出Banach空 间内线性算子的齐性广义逆的统一定义。齐性广义逆包含线性广义逆、单值度量广义 逆.本文证得齐性广义逆存在的充分必要条件.     

求解稀疏相位恢复问题的随机交替方向法(英文)

近年来稀疏相位恢复问题受到了越来越多的关注.本文提出了一种随机交替方法方法求解稀疏相位恢复问题,该算法采用硬阈值追踪算法求解带稀疏约束的最小二乘子问题.大量的数值实验表明,该算法可以通过O(s log n)次测量(理论上最少测量值)稳定的恢复n维s稀疏向量,并且在随机初值下可以获得全局收敛性.     

混合变异粒子群优化算法及其应用

为改善粒子群优化算法在解决复杂优化问题时收敛质量不高的不足,提出了一种改进的粒子群优化算法,即混合变异粒子群优化算法(HMPSO).HMPSO算法采用了带有随机因子的惯性权重取值更新策略,降低了标准粒子群优化算法中由于粒子飞行速度过大而错过最优解的概率,从而加速了算法的收敛速度.此外,通过混合变异进化环节的引入,缓解了...     

A smoothing Levenberg-Marquardt algorithm for solving a class of stochastic linear complementarity problem

In this paper, it is considered for a class of stochastic linear complementarity problems (SLCPs) with finitely many elements. A smoothing Levenberg-Marquardt algorithm is proposed for solving the SLCP. Under suitable conditions, the global convergence and local quadratic convergence of the proposed algorithm is given. Some numerical results are reported in this paper, which confirms the good theoretical properties of the proposed algorithm.     

Grid Restrained Nelder-Mead Algorithm

Probably the most popular algorithm for unconstrained minimization for problems of moderate dimension is the Nelder-Mead algorithm published in 1965. Despite its age only limited convergence results exist. Several counterexamples can be found in the literature for which the algorithm performs badly or even fails. A convergent variant derived from the original Nelder-Mead algorithm is presented. The proposed algorithm's convergence is based on the principle of grid restrainment and therefore does not require sufficient descent as the recent convergent variant proposed by Price, Coope, and Byatt. Convergence properties of the proposed grid-restrained algorithm are analysed. Results of numerical testing are also included and compared to the results of the algorithm proposed by Price et al. The results clearly demonstrate that the proposed grid-restrained algorithm is an efficient direct search method.     

An effective adaptive trust region algorithm for nonsmooth minimization

In this paper, an adaptive trust region algorithm that uses Moreau–Yosida regularization is proposed for solving nonsmooth unconstrained optimization problems. The proposed algorithm combines a modified secant equation with the BFGS update formula and an adaptive trust region radius, and the new trust region radius utilizes not only the function information but also the gradient information. The global convergence and the local superlinear convergence of the proposed algorithm are proven under suitable conditions. Finally, the preliminary results from comparing the proposed algorithm with some existing algorithms using numerical experiments reveal that the proposed algorithm is quite promising for solving nonsmooth unconstrained optimization problems.     

Convergence Properties of the DFP Algorithm for Unconstrained Optimization

In this article, the convergence properties of the DFP algorithm with inexact line searches on uniformly convex functions are investigated. An inexact line search is proposed and the global convergence and superlinear convergence of the DFP algorithm with this line search on uniformly convex functions are proved.     

快速幂法子空间跟踪

子空间跟踪算法是许多工程计算问题的核心.Hua等人将计算特征值问题的幂法扩展为自然幂法子空间跟踪算法.在指出基于秩1矩阵更新的自然幂法的快速实现方案NP3不收敛的同时,应用矩阵求逆引理给出了一种新的快速子空间跟踪算法:快速幂法子空间跟踪算法.仿真实验表明,所提算法是收敛与稳定的,其性能优于或相当于几种常见的快速子空间跟踪算法.     

A new subspace correction method for nonlinear unconstrained convex optimization problems

This paper gives a new subspace correction algorithm for nonlinear unconstrained convex optimization problems based on the multigrid approach proposed by S. Nash in 2000 and the subspace correction algorithm proposed by X. Tai and J. Xu in 2001. Under some reasonable assumptions, we obtain the convergence as well as a convergence rate estimate for the algorithm. Numerical results show that the algorithm is effective.     

A Newton Acceleration of the Weiszfeld Algorithm for Minimizing the Sum of Euclidean Distances

The Weiszfeld algorithm for continuous location problems can be considered as an iteratively reweighted least squares method. It generally exhibits linear convergence. In this paper, a Newton algorithm with similar simplicity is proposed to solve a continuous multifacility location problem with the Euclidean distance measure. Similar to the Weiszfeld algorithm, the main computation can be solving a weighted least squares problem at each iteration. A Cholesky factorization of a symmetric positive definite band matrix, typically with a small band width (e.g., a band width of two for a Euclidean location problem on a plane) is performed. This new algorithm can be regarded as a Newton acceleration to the Weiszfeld algorithm with fast global and local convergence. The simplicity and efficiency of the proposed algorithm makes it particularly suitable for large-scale Euclidean location problems and parallel implementation. Computational experience suggests that the proposed algorithm often performs well in the absence of the linear independence or strict complementarity assumption. In addition, the proposed algorithm is proven to be globally convergent under similar assumptions for the Weiszfeld algorithm. Although local convergence analysis is still under investigation, computation results suggest that it is typically superlinearly convergent.     

A truncated conjugate gradient method with an inexact Gauss-Newton technique for solving nonlinear systems

In this paper, a truncated conjugate gradient method with an inexact Gauss-Newton technique is proposed for solving nonlinear systems.?The iterative direction is obtained by the conjugate gradient method solving the inexact Gauss-Newton equation.?Global convergence and local superlinear convergence rate of the proposed algorithm are established under some reasonable conditions. Finally, some numerical results are presented to illustrate the effectiveness of the proposed algorithm.     

A trust region algorithm with adaptive cubic regularization methods for nonsmooth convex minimization

By using the Moreau-Yosida regularization and proximal method, a new trust region algorithm is proposed for nonsmooth convex minimization. A cubic subproblem with adaptive parameter is solved at each iteration. The global convergence and Q-superlinear convergence are established under some suitable conditions. The overall iteration bound of the proposed algorithm is discussed. Preliminary numerical experience is reported.