A novel three-step implicit iteration process for threeΦ-hemicontractive mapping in the intermediate sense

In this paper,we introduce a three-step composite implicit iteration process for approximating the common fixed point of three uniformly continuous and asymptotically generalizedΦ-hemicontractive mappings in the intermediate sense.We prove that our proposed iteration process converges to the common fixed point of three finite family of asymptotically generalizedΦ-hemicontractive mappings in the intermediate sense.Our results extends,improves and complements several known results in literature.

A Modified Averaging Composite Implicit Iteration Process for Common Fixed Points of a Finite Family of k-Strictly Asymptotically Pseudocontractive Mappings

The composite implicit iteration process introduced by Su and Li [J. Math. Anal. Appl. 320 (2006) 882-891] is modified. A strong convergence theorem for approximation of common fixed points of finite family of k-strictly asymptotically pseudo-contractive mappings is proved in Banach spaces using the modified iteration process.

Time Discretized Variational Iteration Method for the Stochastic Volatility Process with Jumps

A model for both stochastic jumps and volatility for equity returns in the area of option pricing is the stochastic volatility process with jumps (SVPJ). A major advantage of this model lies in the area of mean reversion and volatility clustering between returns and volatility with uphill movements in price asserts. Thus, in this article, we propose to solve the SVPJ model numerically through a discretized variational iteration method (DVIM) to obtain sample paths for the state variable and variance process at various timesteps and replications in order to estimate the expected jump times at various iterates resulting from executing the DVIM as n increases. These jumps help in estimating the degree of randomness in the financial market. It was observed that the average computed expected jump times for the state variable and variance process is moderated by the parameters (variance process through mean reversion), Θ (long-run mean of the variance process), σ (volatility variance process) and λ (constant intensity of the Poisson process) at each iterate. For instance, when = 0.0, Θ = 0.0, σ = 0.0 and λ = 1.0, the state variable cluttered maximally compared to the variance process with less volatility cluttering with an average computed expected jump times of 52.40607869 as n increases in the DVIM scheme. Similarly, when = 3.99, Θ = 0.014, σ = 0.27 and λ = 0.11, the stochastic jumps for the state variable are less cluttered compared to the variance process with maximum volatility cluttering as n increases in the DVIM scheme. In terms of option pricing, the value 52.40607869 suggest a better bargain compared to the value 20.40344029 due to the fact that it yields less volatility rate. MAPLE 18 software was used for all computations in this research.

Partial Iterative Decode of Turbo Codes for On-Board Processing Satellite Platform

There is a contradiction between high processing complexity and limited processing resources when turbo codes are used on the on-board processing(OBP)satellite platform.To solve this problem,this paper proposes a partial iterative decode method for on-board application,in which satellite only carries out limited number of iteration according to the on-board processing resource limitation and the throughput capacity requirements.In this method,the soft information of parity bits,which is not obtained individually in conventional turbo decoder,is encoded and forwarded along with those of information bits.To save downlink transmit power,the soft information is limited and normalized before forwarding.The iteration number and limiter parameters are optimized with the help of EXIT chart and numerical analysis,respectively.Simulation results show that the proposed method can effectively decrease the complexity of onboard processing while achieve most of the decoding gain..

The influence of intimacy on the ’iterative reactions’ during OX-ZEO process for aromatic production

The oxide-zeolite process provides a promising way for one-step production of aromatics from syngas,whereas the reasons for the dramatic effect of intimacy between oxide and zeolite in the composite catalyst on the product selectivity are still unclear. In order to explore the optimal intimacy and the essential influence factors, ZnCrOxcombined with ZSM-5 are employed to prepare the composite catalysts with different distances between the two components by changing the mixing methods. An aromatic selectivity of 74%(with CO conversion to be 16%) is achieved by the composite catalyst when the intimacy is in the range of nanometer. A so-called ‘iterative reactions’ mechanism of intermediates over oxides is then proposed and studied: the intermediate chemical can undergo a hydrogenation reaction on oxide.So the shorter the intermediates stay on oxide, the more of chance for C-C coupling takes place on zeolite to form aromatics. Moreover, the aero-environments of reaction is found to impact on the extent of iterative reaction as well. Therefore, when the intimacy between the two components changes, the extent of iterative reactions vary, resulting in alteration of product distribution. This work provides new insight in understanding the mechanisms during the complex process of OX-ZEO composite catalysis and sheds light to the design of a high-yield catalyst for synthetization of aromatics from syngas.

Filter-based iterative learning control for linear large-scale industrial processes

In the procedure of the steady-state hierarchical optimization with feedback for large-scale industrial processes, a sequence of set-point changes with different magnitudes is carried out on the optimization layer. To improve the dynamic performance of transient response driven by the set-point changes, a filter-based iterative learning control strategy is proposed. In the proposed updating law, a local-symmetric-integral operator is adopted for eliminating the measurement noise of output information,a set of desired trajectories are specified according to the set-point changes sequence, the current control input is iteratively achieved by utilizing smoothed output error to modify its control input at previous iteration, to which the amplified coefficients related to the different magnitudes of set-point changes are introduced. The convergence of the algorithm is conducted by incorporating frequency-domain technique into time-domain analysis. Numerical simulation demonstrates the effectiveness of the proposed strategy,

Accelerating BP-Based Iterative Low-Density Parity-Check Decoding by Modified Vertical and Horizontal Processes

Two modified BP algorithms related to vertical and horizontal processes are proposed to accelerate iterative low-density parity- check （LDPC） decoding over an additive white Gaussian noise （AWGN） channel, where the newly updated extrinsic information is immediately used in the current decoding round. Theoretical analysis and simulation results demonstrate that both the modified approaches provide significant performance improvements over the traditional BP algorithm with almost no additional decoding complexity. The proposed algorithm with modified horizontal process offers even better performance than another algorithm with the modified horizontal process. The two modified BP algorithms are very promising in practical communications since both can achieve an excellent trade-off between the performance and decoding complexity.

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.

Optimal Iterative Learning Control for Batch Processes Based on Linear Time-varying Perturbation Model

为在批的产品质量的追踪的控制的最佳的反复的学习控制(ILC ) 策略处理的 batch-to-batch 被介绍。线性变化时间的不安(LTVP ) 模型在名字的轨道附近为产品质量被造。到模型植物失配的地址问题，在以前的成批处理的模型预言错误为当前的成批处理被加到模型预言。然后追踪错误转变模型能被造，并且有直接错误反馈的 ILC 法律明确地被获得。一条严密定理被建议，到证明在 ILC 下面追踪错误的集中。建议方法论在一个典型的批反应堆和轨道追踪的表演被 ILC 逐渐地改进的结果表演上被说明。

Iterative Learning Model Predictive Control for a Class of Continuous/Batch Processes

一个反复的学习模型预兆的控制(ILMPC ) 技术被用于 continuous/batch 过程的一个班。如此的过程被产生周期的强壮的骚乱到连续过程的批过程的操作描绘，传统的规章的控制器是不能的消除这些周期的骚乱。ILMPC 集成处理重复信号和灵活性的反复的学习控制(ILC ) 的特征为预兆的控制(MPC ) 建模。由联机监视，批的操作地位处理，事件驱动为批的反复的学习算法重复骚乱被开始，软限制被调整象可行区域及时离开需要的操作地区。一个工业应用程序的结果证明建议 ILMPC 方法为 continuous/batch 进程的一个类是有效的。

An Anticipatory Terminal Iterative Learning Control Approach with Applications to Constrained Batch Processes

This work presents an anticipatory terminal iterative learning control scheme for a class of batch processes, where only the final system output is measurable and the control input is constant in each operations. The proposed approach works well with input constraints provided that the desired control input with respect to the desired trajectory is within the saturation bound. The tracking error convergence is established with rigorous mathematical analysis. Simulation results are provided to show the effectiveness of the proposed approach.

An LMI Method to Robust Iterative Learning Fault-tolerant Guaranteed Cost Control for Batch Processes

Based on an equivalent two-dimensional Fornasini-Marchsini model for a batch process in industry, a closed-loop robust iterative learning fault-tolerant guaranteed cost control scheme is proposed for batch processes with actuator failures. This paper introduces relevant concepts of the fault-tolerant guaranteed cost control and formulates the robust iterative learning reliable guaranteed cost controller (ILRGCC). A significant advantage is that the proposed ILRGCC design method can be used for on-line optimization against batch-to-batch process uncertainties to realize robust tracking of set-point trajectory in time and batch-to-batch sequences. For the convenience of implementation, only measured output errors of current and previous cycles are used to design a synthetic controller for iterative learning control, consisting of dynamic output feedback plus feed-forward control. The proposed controller can not only guarantee the closed-loop convergency along time and cycle sequences but also satisfy the H∞performance level and a cost function with upper bounds for all admissible uncertainties and any actuator failures. Sufficient conditions for the controller solution are derived in terms of linear matrix inequalities (LMIs), and design procedures, which formulate a convex optimization problem with LMI constraints, are presented. An example of injection molding is given to illustrate the effectiveness and advantages of the ILRGCC design approach.

A PARALLEL COMPUTATION SCHEME FOR IMPLICIT RUNGE-KUTTA METHODS AND THE ITERATIVELY B-CONVERGENCE OF ITS NEWTON ITERATIVE PROCESS

In this paper, based on the implicit Runge-Kutta(IRK) methods, we derive a class of parallel scheme that can be implemented on the parallel computers with Ns(N is a positive even number) processors efficiently, and discuss the iteratively B-convergence of the Newton iterative process for solving the algebraic equations of the scheme, secondly we present a strategy providing initial values parallelly for the iterative process. Finally, some numerical results show that our parallel scheme is higher efficient as N is not so large.

Arranging transient process used in iterative learning control system

Considering the same initial state error in each repetitive operation in the iterative learning system, a method of arranging the transient process is given. During the current iteration, the system will track the transient function firstly, and then the expected trajectory. After several iterations, the learning system output will trend to the arranged curve, which has avoided the effect of the initial error on the controller. Also the transient time can be changed as you need, which makes the designing simple and the operation easy. Then the detailed designing steps are given via the robot system. At last the simulation of the robot system is given, which shows the validity of the method.

ISHIKAWA ITERATIVE PROCESS IN UNIFORMLY SMOOTH BANACH SPACES

Let E be a uniformly smooth Banach space, K be a nonempty closed convex subset of E, and suppose: T: K --> K is a continuous Phi-strongly pseudocontractive operator with a bounded range. Using a new analytical method, under general cases, the Ishikawa iterative process {x(n)} converges strongly to the unique fixed point x* of the operator T were proved. The paper generalizes and extends a lot of recent corresponding results.

Topological Order Value Iteration Algorithm for Solving Probabilistic Planning

AI researchers typically formulated probabilistic planning under uncertainty problems using Markov Decision Processes (MDPs).Value Iteration is an inef?cient algorithm for MDPs, because it puts the majority of its effort into backing up the entire state space, which turns out to be unnecessary in many cases. In order to overcome this problem, many approaches have been proposed. Among them, LAO*, LRTDP and HDP are state-of-the-art ones. All of these use reach ability analysis and heuristics to avoid some unnecessary backups. However, none of these approaches fully exploit the graphical features of the MDPs or use these features to yield the best backup sequence of the state space. We introduce an improved algorithm named Topological Order Value Iteration (TOVI) that can circumvent the problem of unnecessary backups by detecting the structure of MDPs and backing up states based on topological sequences. The experimental results demonstrate the effectiveness and excellent performance of our algorithm.

On the Deepest Fallacy in the History of Mathematics: The Denial of the Postulate about the Approximation Nature of a Simple-Iteration Method and Iterative Derivation of Cramer’s Formulas

Contrary to the opinion about approximation nature of a simple-iteration method, the exact solution of a system of linear algebraic equations (SLAE) in a finite number of iterations with a stationary matrix is demonstrated. We present a theorem and its proof that confirms the possibility to obtain the finite process and imposes the requirement for the matrix of SLAE. This matrix must be unipotent, i.e. all its eigenvalues to be equal to 1. An example of transformation of SLAE given analytically to the form with a unipotent matrix is presented. It is shown that splitting the unipotent matrix into identity and nilpotent ones results in Cramer’s analytical formulas in a finite number of iterations.

Algorithm of Iterative Process for Some Mappings and Iterative Solution of Some Diffusion Equation

In Hilbert spaces , through improving some corresponding conditions in some literature and extending some recent relevent results, a strong convergence theorem of some implicit iteration process for pesudocon-traction mappings and explicit iteration process for nonexpansive mappings were established. And by using the result, some iterative solution for some equation of response diffusion were obtained.

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.

A Multi-Band Speech Enhancement Algorithm Exploiting Iterative Processing for Enhancement of Single Channel Speech

This paper proposes a multi-band speech enhancement algorithm exploiting iterative processing for enhancement of single channel speech. In the proposed algorithm, the output of the multi-band spectral subtraction (MBSS) algorithm is used as the input signal again for next iteration process. As after the first MBSS processing step, the additive noise transforms to the remnant noise, the remnant noise needs to be further re-estimated. The proposed algorithm reduces the remnant musical noise further by iterating the enhanced output signal to the input again and performing the operation repeatedly. The newly estimated remnant noise is further used to process the next MBSS step. This procedure is iterated a small number of times. The proposed algorithm estimates noise in each iteration and spectral over-subtraction is executed independently in each band. The experiments are conducted for various types of noises. The performance of the proposed enhancement algorithm is evaluated for various types of noises at different level of SNRs using, 1) objective quality measures: signal-to-noise ratio (SNR), segmental SNR, perceptual evaluation of speech quality (PESQ);and 2) subjective quality measure: mean opinion score (MOS). The results of proposed enhancement algorithm are compared with the popular MBSS algorithm. Experimental results as well as the objective and subjective quality measurement test results confirm that the enhanced speech obtained from the proposed algorithm is more pleasant to listeners than speech enhanced by classical MBSS algorithm.