Iterative Processes with Errors for Generalized Set-Valued φ-Hemi-contractive Mapping in Banach Spaces

A new conception of generalized set-valued Ф-hemi-contractive mapping in Banach spaces is presented. Some strong convergence theorems of Ishikawa and Mann iterative approximation with errors is proved. The results in this paper improve and extend the earlier results.

ON THE CONVERGENCE PROBLEMS OF ISHIKAWA AND MANN ITERATIVE PROCESSES WITH ERROR FOR Φ-PSEUDO CONTRACTIVE TYPE MAPPINGS

The purpose of this paper is to introduce the concept of Φ_pseudo contractive type mapping and to study the convergence problem of Ishikawa and Mann iterative processes with error for this kind of mappings. The results presented in this paper improve and extend many authors'recent results.

Iterative Approximation with Errors for Generalized Set-Valued Strongly Accretive Mapping in Banach Spaces

A new concept of generalized set-valued strongly accretive mappings in Banach spaces was given and some strong convergence theorems of Ishikawa and Mann iterative process with errors approximation methods by Huang et al. was proved. The results presented in this paper improve and extend the earlier results obtained by Huang et al.

Existence and numerical approximation of a solution to frictional contact problem for electro-elastic materials

In this paper,a frictional contact problem between an electro-elastic body and an electrically conductive foundation is studied.The contact is modeled by normal compliance with finite penetration and a version of Coulomb’s law of dry friction in which the coefficient of friction depends on the slip.In addition,the effects of the electrical conductivity of the foundation are taken into account.This model leads to a coupled system of the quasi-variational inequality of the elliptic type for the displacement and the nonlinear variational equation for the electric potential.The existence of a weak solution is proved by using an abstract result for elliptic variational inequalities and a fixed point argument.Then,a finite element approximation of the problem is presented.Under some regularity conditions,an optimal order error estimate of the approximate solution is derived.Finally,a successive iteration technique is used to solve the problem numerically and a convergence result is established.

Carlson iterating rational approximation and performance analysis of fractional operator with arbitrary order

The performance analysis of the generalized Carlson iterating process,which can realize the rational approximation of fractional operator with arbitrary order,is presented in this paper.The reasons why the generalized Carlson iterating function possesses more excellent properties such as self-similarity and exponential symmetry are also explained.K-index,P-index,O-index,and complexity index are introduced to contribute to performance analysis.Considering nine different operational orders and choosing an appropriate rational initial impedance for a certain operational order,these rational approximation impedance functions calculated by the iterating function meet computational rationality,positive reality,and operational validity.Then they are capable of having the operational performance of fractional operators and being physical realization.The approximation performance of the impedance function to the ideal fractional operator and the circuit network complexity are also exhibited.

Three-step Iterations with Errors for Nonlinear Strongly Accretive Operator Equations

In this paper, we suggest and analyse a three-step iterative scheme with errors for solving nonlinear strongly accretive operator equation Tx = f without the Lipshitz condition. The results presented in this paper improve and extend current results in the more general setting.

An Implicit Iteration Process with Errors for a Finite Family of r-strictly Asymptotically Pseudocontractive Mappings

In this paper, we will establish several strong convergence theorems for the approximation of common fixed points of r-strictly asymptotically pseudocontractive mappings in uniformly convex Banach spaces using the modiied implicit iteration sequence with errors, and prove the necessary and sufficient conditions for the convergence of the sequence. Our results generalize, extend and improve the recent work, in this topic.

Run-to-run product quality control of batch processes

Batch processes have been increasingly used in the production of low volume and high value added products. Consequently, optimization control in batch processes is crucial in order to derive the maximum benefit. In this paper, a run-to-run product quality control based on iterative learning optimization control is developed. Moreover, a rigorous theorem is proposed and proven in this paper, which states that the tracking error under the optimal iterative learning control （ILC） law can converge to zero. In this paper, a typical nonlinear batch continuous stirred tank reactor （CSTR） is considered, and the results show that the performance of trajectory tracking is gradually improved by the ILC.

双向聚类迭代的协同过滤推荐算法

协同过滤是电子商务推荐系统中广泛采用的技术,然而数据稀疏性会影响协同过滤的推荐质量。针对数据稀疏问题提出一种双向聚类迭代的协同过滤推荐算法,对初始得到的用户聚类和项目聚类进行交叉迭代调整,使得聚类簇达到较为稳定的状态。调整后聚类簇的内聚性更强,类之间的区分度更大。实验表明,在调整后的聚类簇中查找邻居将更加准确,可以有效解决数据稀疏问题的影响,有利于提高推荐的准确性。

带误差项的Ishikawa迭代过程的注记

使用新的逼近技巧,研究了一致光滑的Banach空间中具有Lipschitz强增生算子的带误差项的Ishikawa迭代过程的收敛性问题.

一种基于混合误差梯度下降算法的过程神经网络训练

针对过程神经网络(PNN)单一训练算法自适应调整能力差、缺乏对学习性质有效控制的问题,提出一种梯度下降与牛顿迭代相结合的求解算法——混合误差梯度下降算法.在训练初始阶段,基于网络训练目标函数,采用梯度下降法进行迭代寻优,只需计算目标函数一阶导数数值公式,复杂度低且误差下降快;当梯度下降法学习效率降低时,引入牛顿迭代法,并将梯度下降法的训练结果作为初始参数代入目标函数,使问题转化为求解非线性方程组,不需要一维搜索而提高网络训练效率.通过学习效率分析自适应调节两种算法的切换,直至满足停机条件.将其应用于时变信号模式分类,实验结果表明,该算法较大地提高PNN训练效率.

一种基于图像处理的激光光斑圆度测量方法

介绍圆度误差的评定方法,在图像处理的基础上,针对圆形激光光斑,设计出一种通过计算光斑轮廓的最大内接圆得出其圆度误差的算法。首先,利用图像处理算法对激光图像进行二值化处理,提取出二值图像中的激光轮廓,对轮廓进行膨胀腐蚀运算后,采用中轴变换和剪枝处理得到光滑、闭合的轮廓曲线。然后通过矢量迭代法计算光斑轮廓内最大内接圆的圆心位置。最后得出激光轮廓的圆度误差值。矢量迭代法是对三角形迭代法的改进,该算法容易选择初值,复杂度低,准确性高并能够有效地解决局部极值问题。经过对实际激光图像进行测试表明,该算法快捷稳定。

动量项技术在带钢热连轧负荷分配中的应用

将源于BP人工神经网络改进策略的动量项技术引入到带钢热连轧负荷分配中来,提出了误差补偿迭代算法,介绍了该算法的推导过程,并对算法的合理性进行了分析。基于误差补偿迭代算法及传统的Newton-Raph-son法,开发了带钢热连轧精轧过程设定系统软件。离线模拟计算结果表明,与Newton-Raphson法相比,误差补偿迭代算法对初始厚度分布的要求比较宽松,有利于新产品的开发,具有良好的在线应用前景。

舰艇进水过程中的不沉性指标计算及实验研究

为了描述舰艇进水过程中的不沉性指标随时间的变化关系,文章首先建立了进水过程的姿态参数时域微分模型;然后,分析了国外提出的流量差值迭代法的不足之处,建立了基于"四阶龙格—库塔"的数值求解算法,分析了其求解的物理意义,并进行了船模实验验证。最后,以某船模为对象进行了进水过程中浮性和稳性指标的仿真计算,计算结果揭示了进水过程可能会比进水稳定平衡状态更加危险的现象。

接近非相干水声通信信道容量的信号处理算法

恶劣情况下的非相干水声通信信道模型为随机相位Rayleigh衰落，推导了该模型的信道容量曲线。为实现接近非相干信道容量的可靠通信，提出多进制低密度校验码（LDPC）和恒重码级联码的多进制非相干概率域迭代处理算法。在信道幅度和相位完全未知的情况下，根据矩估计得到信号和噪声频点幅度的统计参量，进而得到恒重码的码字后验概率，再对多进制LDPC码进行因子图迭代译码。仿真证明本算法与现有的最大能量检测非迭代译码算法相比，与信道容量曲线的差距从4．5dB缩小至1．5dB。给出了实际海试湖试通信效果，频段为6—10kHz，数据速率为357bps，海试时近似垂直通信距离为5km，湖试时水平通信距离近3km、多径超过50mS，两种情况下无差错通信的信噪比门限为2dB，验证了本算法的优势。

Φ-伪压缩型映象的具误差的Ishikawa和Mann迭代程序的收敛性问题

引入Φ＿ 伪压缩型映象的概念，并研究了此类映象的具误差的Ｉｓｈｉｋａｗａ 和Ｍａｎｎ 迭代程序的收敛性问题· 本文结果改进和发展了许多人的最新结果·

赋范空间中Ф-半压缩型映象的不动点的迭代逼近

使用赋范空间中一个不等式以及某些分析技巧，证明了赋范线性空间中中半压缩映象的不动点的迭代过程的若干收敛定理，改进和扩展了近期相应的一些结果．

算子方程x+THx=f的带误差的Ishikawa迭代解

给出了L-S-次逆增生算子H的定义.在一致光滑Banach空间中建立了收敛于方程x+THx=f的带误差的Ishikawa迭代序列,其中T是k-次增生算子,H是L-S-次逆增生算子,推广和改进了一些已有结果.

增生算子方程的具误差的Ishikawa迭代序列的强收敛定理

本文研究了Banach空间中Lipschitz的增生算子T的方程的解的迭代逼近问题.利用Ishikawa迭代法,证明了具误差的Ishikawa迭代序列强收敛到方程的唯一解,得到了一般的收敛率估计式.

渐近非扩张映象迭代序列的收敛性

用新方法研究了Banach空间中渐近非扩张映象不动点的迭代逼近问题,所得结果改进和发展了前人的结果。