• Title, Summary, Keyword: iterative method

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Estimation of learning gain in iterative learning control using neural networks

  • Choi, Jin-Young;Park, Hyun-Joo
    • 제어로봇시스템학회:학술대회논문집
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    • pp.91-94
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    • 1996
  • This paper presents an approach to estimation of learning gain in iterative learning control for discrete-time affine nonlinear systems. In iterative learning control, to determine learning gain satisfying the convergence condition, we have to know the system model. In the proposed method, the input-output equation of a system is identified by neural network refered to as Piecewise Linearly Trained Network (PLTN). Then from the input-output equation, the learning gain in iterative learning law is estimated. The validity of our method is demonstrated by simulations.

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STRONG CONVERGENCE OF MONOTONE CQ ITERATIVE PROCESS FOR ASYMPTOTICALLY STRICT PSEUDO-CONTRACTIVE MAPPINGS

  • Zhang, Hong;Su, Yongfu;Li, Mengqin
    • Journal of applied mathematics & informatics
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    • v.27 no.3_4
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    • pp.763-771
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    • 2009
  • T.H. Kim, H.K. Xu, [Convergence of the modified Mann's iteration method for asymptotically strict pseudo-contractions, Nonlinear Anal.(2007),doi:l0.l016/j.na.2007.02.029.] proved the strong convergence for asymptotically strict pseudo-contractions by the classical CQ iterative method. In this paper, we apply the monotone CQ iterative method to modify the classical CQ iterative method of T.H. Kim, H.K. Xu, and to obtain the strong convergence theorems for asymptotically strict pseudo-contractions. In the proved process of this paper, Cauchy sequences method is used, so we complete the proof without using the demi-closedness principle, Opial's condition or others about weak topological technologies. In addition, we use a ingenious technology to avoid defining that F(T) is bounded. On the other hand, we relax the restriction on the control sequence of iterative scheme.

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PRECONDITIONED GAUSS-SEIDEL ITERATIVE METHOD FOR Z-MATRICES LINEAR SYSTEMS

  • Shen, Hailong;Shao, Xinhui;Huang, Zhenxing;Li, Chunji
    • Bulletin of the Korean Mathematical Society
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    • v.48 no.2
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    • pp.303-314
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    • 2011
  • For Ax = b, it has recently been reported that the convergence of the preconditioned Gauss-Seidel iterative method which uses a matrix of the type P = I + S (${\alpha}$) to perform certain elementary row operations on is faster than the basic Gauss-Seidel method. In this paper, we discuss the adaptive Gauss-Seidel iterative method which uses P = I + S (${\alpha}$) + $\bar{K}({\beta})$ as a preconditioner. We present some comparison theorems, which show the rate of convergence of the new method is faster than the basic method and the method in [7] theoretically. Numerical examples show the effectiveness of our algorithm.

A NEWTON-IMPLICIT ITERATIVE METHOD FOR NONLINEAR INVERSE PROBLEMS

  • Meng, Zehong;Zhao, Zhenyu
    • Journal of applied mathematics & informatics
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    • v.29 no.3_4
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    • pp.909-920
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    • 2011
  • A regularized Newton method for nonlinear ill-posed problems is considered. In each Newton step an implicit iterative method with an appropriate stopping rule is proposed and analyzed. Under certain assumptions on the nonlinear operator, the convergence of the algorithm is proved and the algorithm is stable if the discrepancy principle is used to terminate the outer iteration. Numerical experiment shows the effectiveness of the method.

Computer Algorithm for the Loadflow of the DC Traction Power Supply System (도시철도의 DC급전시스템 해석 알고리즘)

  • 정상기;홍재승
    • Proceedings of the KSR Conference
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    • pp.78-85
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    • 2000
  • Computer algorithms for the loadflow of the DC traction power supply system are examined. Algorithms to solve the nodal equation are reviewed and the two iterative methods to solve the nonlinear nature of the loadflow are analyzed and tested, which are so called conductance matrix method and current vector iterative mettled. The result of the analysis tells that the current vector iterative method makes faster convergency and needs less computing time, and it is verified by the test running of the programs based on each of the iterative methods.

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A HYBRID ITERATIVE METHOD OF SOLUTION FOR MIXED EQUILIBRIUM AND OPTIMIZATION PROBLEMS

  • Zhang, Lijuan;Chen, Jun-Min
    • East Asian mathematical journal
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    • v.26 no.1
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    • pp.25-38
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    • 2010
  • In this paper, we introduce a hybrid iterative method for finding a common element of the set of solutions of a mixed equilibrium problem, the set of common mixed points of finitely many nonexpansive mappings and the set of solutions of the variational inequality for an inverse strongly monotone mapping in a Hilbert space. We show that the iterative sequences converge strongly to a common element of the three sets. The results extended and improved the corresponding results of L.-C.Ceng and J.-C.Yao.

High Performance Hybrid Direct-Iterative Solution Method for Large Scale Structural Analysis Problems

  • Kim, Min-Ki;Kim, Seung-Jo
    • International Journal of Aeronautical and Space Sciences
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    • v.9 no.2
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    • pp.79-86
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    • 2008
  • High performance direct-iterative hybrid linear solver for large scale finite element problem is developed. Direct solution method is robust but difficult to parallelize, whereas iterative solution method is opposite for direct method. Therefore, combining two solution methods is desired to get both high performance parallel efficiency and numerical robustness for large scale structural analysis problems. Hybrid method mentioned in this paper is based on FETI-DP (Finite Element Tearing and Interconnecting-Dual Primal method) which has good parallel scalability and efficiency. It is suitable for fourth and second order finite element elliptic problems including structural analysis problems. We are using the hybrid concept of theses two solution method categories, combining the multifrontal solver into FETI-DP based iterative solver. Hybrid solver is implemented for our general structural analysis code, IPSAP.

FEM-BEM iterative coupling procedures to analyze interacting wave propagation models: fluid-fluid, solid-solid and fluid-solid analyses

  • Soares, Delfim Jr.
    • Coupled systems mechanics
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    • v.1 no.1
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    • pp.19-37
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    • 2012
  • In this work, the iterative coupling of finite element and boundary element methods for the investigation of coupled fluid-fluid, solid-solid and fluid-solid wave propagation models is reviewed. In order to perform the coupling of the two numerical methods, a successive renewal of the variables on the common interface between the two sub-domains is performed through an iterative procedure until convergence is achieved. In the case of local nonlinearities within the finite element sub-domain, it is straightforward to perform the iterative coupling together with the iterations needed to solve the nonlinear system. In particular, a more efficient and stable performance of the coupling procedure is achieved by a special formulation that allows to use different time steps in each sub-domain. Optimized relaxation parameters are also considered in the analyses, in order to speed up and/or to ensure the convergence of the iterative process.

Iterative Tuning of PID Controller by Fuzzy Indirect Reasoning and a Modified Zigler-Nichols Method (퍼지 간접추론법과 수정형 지글러-니콜스법에 의한 비례-적분-미분 제어기의 점진적 동조)

  • Kim, S.D.
    • Journal of the Korean Society for Precision Engineering
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    • v.13 no.5
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    • pp.74-83
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    • 1996
  • An iterative tuning technique is derived for PID controllers which are widely used in industries. The tuning algorithm is based upon a fuzzy indirect reasoning method and an iterative technique. The PID gains for the first tuning action are determined by a method which is modified from the Ziegler-Nichols step response method. The first PID gains are determined to obtain a control performance so close to a design performance that the following tuning process can be made effectively. The design paramaters are given as time-domain variables which human is familiar with. The results of simulation studies show that the proposed tuning method can produce an effective tuning for arbitrary design performances.

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The Iterated Ritz Method: Basis, implementation and further development

  • Dvornik, Josip;Lazarevic, Damir;Uros, Mario;Novak, Marta Savor
    • Coupled systems mechanics
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    • v.7 no.6
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    • pp.755-774
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    • 2018
  • The Ritz method is known as very successful strategy for discretizing continuous problems, but it has never been used for solving systems of algebraic equations. The Iterated Ritz Method (IRM) is a novel iterative solver based on the discretized Ritz procedure applied at each iteration step. With an appropriate choice of coordinate vectors, the method may be efficient in linear, nonlinear and optimization problems. Additionally, some iterative methods can be explained as special cases of this approach, which helps to understand advantages and limitations of these methods and gives motivation for their improvement in sense of IRM. In this paper, some ideas for generation of efficient coordinate vectors are presented. The algorithm was developed and tested independently and then implemented into the open source program FEAP. Method has been successfully applied to displacement based (even ill-conditioned) models of structural engineering practice. With this original approach, a new iterative solution strategy has been opened.