一致L-Lipschitz的渐近拟伪压缩型映象迭代收敛的充要条件

设E是任意的实Banach空间,C是E的非空凸子集(C可以是E的无界子集),T:C→C是→致L-Lipschitz的渐近拟伪压缩型映象,在对参数的一些限制条件下,该文给出了带误差的修改的Ishikawa迭代序列强收敛于T的不动点的充要条件.     

利用再生核解一类变系数偏微分方程

如何求解偏微分方程,已经成为各个领域内非常重视的课题.在再生核空间中,给出了变系数偏微分方程的级数形式精确解,为了数值计算,给出了一个迭代方法,并证明了迭代方法的收敛性.数值算例表明本文方法是有效的而且具有良好的实用性.     

Iterative Algorithms for Multiscale State Estimation, Part 2: Numerical Investigations

Usually, direct methods are employed for the solution of linear systems arising in the context of optimization. However, motivated by the potential of multiscale refinement schemes for large problems of dynamic state estimation, we investigate in this paper the application of iterative solvers based on the concepts developed in Ref. 1. Specifically, we explore the effect of different system reductions for various Krylov-space iteration methods as well as three concepts of preconditioning. The first one is the normalization of states and outputs, which also favors error analysis. Next, diagonal scale-dependent preconditioners are compared; they all bound the condition numbers independently of the refinement scale, but exhibit significant quantitative differences. Finally, the effect of the regularization parameter on condition numbers and iteration numbers is analyzed. It turns out that a so-called simplified Uzawa scheme with Jacobi preconditioning and suitable regularization parameter is most efficient. The experiments also reveal that further improvements are necessary.     

ON THE ITERATIVE APPROXIMATION PROBLEM OF FIXED POINTS FOR ASYMPTOTICALLY NONEXPANSIVE TYPE MAPPINGS IN BANACH SPACES

ＩｎｔｒｏｄｕｃｔｉｏｎＴｈｒｏｕｇｈｏｕｔｔｈｉｓｐａｐｅｒｗｅａｓｓｕｍｅｔｈａｔＥｉｓａｒｅａｌＢａｎａｃｈｓｐａｃｅ ,Ｅ ｉｓｔｈｅｄｕａｌｓｐａｃｅｏｆＥ ,ＤｉｓａｎｏｎｅｍｐｔｙｓｕｂｓｅｔｏｆＥａｎｄＪ:Ｅ → 2 Ｅ ｉｓｔｈｅｎｏｒｍａｌｉｚｅｄｄｕａｌｉｔｙｍａｐｐｉｎｇｄｅｆｉｎｅｄｂｙＪ(ｘ) =ｆ∈Ｅ :〈ｘ ,ｆ〉 =‖ｘ‖·‖ｆ‖ ,　‖ｆ‖ =‖ｘ‖ (ｘ∈Ｅ) .　　Ｄｄｆｉｎｉｔｉｏｎ 1 1　ＬｅｔＴ :Ｄ →Ｄｂｅａｍａｐｐｉｎｇ1 )Ｔｉｓｓａｉｄｔｏｂｅａｓｙｍｐｔｏｔｉｃａｌｌｙｎｏ…     

计算方程重根及其重数的算法

给出一种计算方程重根及重数的迭代算法,分别具有平方收敛和线性收敛.(i)迭代:x_(n+1)=x_n-f x_n (f'(x_n))/((f'(x_n))~2-(f(x_n)f~n(x_n)),m_n=((f'(x_n)))~2/((f'(x_n))~2-f(xn_)f″(x_n)),n=0,1,2,…,重数m≈mn;(ii)加速迭代:x_(n+1)=x_n-(f~((m-1))(x_n))/(f(~m)(x_n)).     

Phase imaging with rotating illumination

A modified extended-ptychographical-iterative-engine （ePIE） algorithm is proposed to overcome the dis- advantages of ePIE technique and reduce the influence of stage hysteresis or backlash error. The exit wave of a rotatable ＂screen＂ illuminated by plane wave is used as the illumination on the specimen, and the complex transmission functions of the rotatable object and specimen can be simultaneously reconstructed. Compared with the standard x - y scanning PIE algorithm, the proposed algorithm can completely avoid the influence of stage hysteresis （or backlash error）. The proposed algorithm also has higher convergence s!oeed and better accuracy than the standard PIE algorithm.     

含H-单调映象的完全广义非线性变分包含

引入和研究了一类新的完全广义非线性变分包含.在Hilbert空间中利用与H-单调映象相联系的预解算子的性质,对完全广义非线性变分包含建立了解的存在性定理和构造了一种新的迭代算法,证明了由此算法生成的迭代序列强收敛于精确解.其算法和结果是最近文献中相应算法和结果的改进和推广.     

一种新的稳健波束形成算法及其一维搜索策略

存在条件失配时自适应波束形成器的性能急剧下降,凸优化技术的引入使稳健波束形成器的设计更加灵活,但同时带来了计算复杂度的增加和工程实现上的困难.针对上述问题,提出了一种基于最小二乘估计的稳健波束形成算法,并推导得到一种基于一维搜索的求解方法.首先利用广义旁瓣对消器的结构将标准Capon波束形成器转化为稳健最小二乘问题,并将该问题转化为二阶锥规划的形式.为了减少计算量,利用二阶锥规划问题的原始问题和对偶问题的关系,将求解过程转化为一维搜索,并利用牛顿迭代法获得最优解,从而获得与标准Capon波束形成相近的计算复杂度.仿真分析表明,该算法具有良好的抗导向矢量失配和快拍数不足的稳健性.     

基于迭代学习的离散切换系统故障估计

针对一类具有任意切换序列的离散切换系统的故障估计问题,提出了一种新的故障估计算法.该算法利用引入的虚拟故障信号构建出故障估计器,并利用残差信号通过迭代学习方法对引入的虚拟故障进行逐次修正.使虚拟故障随着迭代次数的增加逐渐逼近实际故障.利用压缩映射方法严格证明了算法在各个子区间上的收敛性,给出了算法的收敛条件.理论分析表明,所提算法能够在有限区间上精确估计出切换系统发生的不同类型故障.最后通过仿真实验进一步验证了所提算法的有效性.     

抗混叠轮廓波域采用压缩感知的云图融合方法

提出一种采用压缩感知的云图融合方法.该方法针对传统轮廓波存在频谱混叠的缺点,结合抗混叠塔式滤波器组和方向滤波器组,构造出一种抗混叠的轮廓波变换,并将其引入压缩感知中的稀疏表示环节,将云图分解成稠密和稀疏两部分|对稠密成份采用传统方法进行融合,而对稀疏成份,则在压缩感知框架下,通过少数线性测量的融合,并采用二步迭代收缩的图像重构算法,在迭代时利用前面两个估计值更新当前值,得到融合结果.实验表明,该方法的融合结果无论在视觉质量及定量指标上都明显优于传统方法,有利于揭示全面的天气信息.