• Title/Summary/Keyword: order of convergence

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A Study on the Second-order Iterative Learning Control Algorithm with Feedback (궤환을 갖는 2차 반복 학습제어 알고리즘에 관한 연구)

  • Huh, Kyung-Moo
    • The Transactions of the Korean Institute of Electrical Engineers A
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    • v.48 no.5
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    • pp.629-635
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    • 1999
  • A second-order iterative learning control algorithm with feedback is proposed in this paper, in which a feedback term is added in the learning control scheme for the enhancement of convergence speed and robustness to disturbances or system parameter variations. The convergence proof of the proposed algorithm is givenl, and the sufficient condition for the convergence of the algorithm is provided. And it also includes the discussions about the convergence performance of the algorithm when the initial condition at the beginning of each iteration differs from the previous value of the initial. Simulation results show the validity and efficiency of the proposed algorithm.

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ON THE SEMI-LOCAL CONVERGENCE OF CONTRAHARMONIC-MEAN NEWTON'S METHOD (CHMN)

  • Argyros, Ioannis K.;Singh, Manoj Kumar
    • Communications of the Korean Mathematical Society
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    • v.37 no.4
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    • pp.1009-1023
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    • 2022
  • The main objective of this work is to investigate the study of the local and semi-local convergence of the contraharmonic-mean Newton's method (CHMN) for solving nonlinear equations in a Banach space. We have performed the semi-local convergence analysis by using generalized conditions. We examine the theoretical results by comparing the CHN method with the Newton's method and other third order methods by Weerakoon et al. using some test functions. The theoretical and numerical results are also supported by the basins of attraction for a selected test function.

INEXACT-NEWTON METHOD FOR SOLVING OPERATOR EQUATIONS IN INFINITE-DIMENSIONAL SPACES

  • Liu Jing;Gao Yan
    • Journal of applied mathematics & informatics
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    • v.22 no.1_2
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    • pp.351-360
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    • 2006
  • In this paper, we develop an inexact-Newton method for solving nonsmooth operator equations in infinite-dimensional spaces. The linear convergence and superlinear convergence of inexact-Newton method under some conditions are shown. Then, we characterize the order of convergence in terms of the rate of convergence of the relative residuals. The present inexact-Newton method could be viewed as the extensions of previous ones with same convergent results in finite-dimensional spaces.

EXPONENTIALLY FITTED NUMERICAL SCHEME FOR SINGULARLY PERTURBED DIFFERENTIAL EQUATIONS INVOLVING SMALL DELAYS

  • ANGASU, MERGA AMARA;DURESSA, GEMECHIS FILE;WOLDAREGAY, MESFIN MEKURIA
    • Journal of applied mathematics & informatics
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    • v.39 no.3_4
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    • pp.419-435
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    • 2021
  • This paper deals with numerical treatment of singularly perturbed differential equations involving small delays. The highest order derivative in the equation is multiplied by a perturbation parameter 𝜀 taking arbitrary values in the interval (0, 1]. For small 𝜀, the problem involves a boundary layer of width O(𝜀), where the solution changes by a finite value, while its derivative grows unboundedly as 𝜀 tends to zero. The considered problem contains delay on the convection and reaction terms. The terms with the delays are approximated using Taylor series approximations resulting to asymptotically equivalent singularly perturbed BVPs. Inducing exponential fitting factor for the term containing the singular perturbation parameter and using central finite difference for the derivative terms, numerical scheme is developed. The stability and uniform convergence of difference schemes are studied. Using a priori estimates we show the convergence of the scheme in maximum norm. The scheme converges with second order of convergence for the case 𝜀 = O(N-1) and for the case 𝜀 ≪ N-1, the scheme converge uniformly with first order of convergence, where N is number of mesh intervals in the domain discretization. We compare the accuracy of the developed scheme with the results in the literature. It is found that the proposed scheme gives accurate result than the one in the literatures.

Effect of annealing temperature on the electrical characteristics of P-doped ZnO thin films

  • Kim, Jun-Kwan;Lim, Jung-Wook;Kim, Hyun-Tak;Kim, Sang-Hun;Yun, Sun-Jin
    • 한국정보디스플레이학회:학술대회논문집
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    • 2007.08b
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    • pp.1622-1624
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    • 2007
  • In order to realize effective p-type doping in ZnO thin films, ZnO films were deposited on P-doped Silayers by RF-magnetron sputter deposition technique and annealed at various temperatures. The result indicated that ZnO film annealed at $700^{\circ}C$ showed p-type conduction with a high carrier concentration in the order of $10^{19}\;cm^{-3}$.

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Accurate Pig Detection for Video Monitoring Environment (비디오 모니터링 환경에서 정확한 돼지 탐지)

  • Ahn, Hanse;Son, Seungwook;Yu, Seunghyun;Suh, Yooil;Son, Junhyung;Lee, Sejun;Chung, Yongwha;Park, Daihee
    • Journal of Korea Multimedia Society
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    • v.24 no.7
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    • pp.890-902
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    • 2021
  • Although the object detection accuracy with still images has been significantly improved with the advance of deep learning techniques, the object detection problem with video data remains as a challenging problem due to the real-time requirement and accuracy drop with occlusion. In this research, we propose a method in pig detection for video monitoring environment. First, we determine a motion, from a video data obtained from a tilted-down-view camera, based on the average size of each pig at each location with the training data, and extract key frames based on the motion information. For each key frame, we then apply YOLO, which is known to have a superior trade-off between accuracy and execution speed among many deep learning-based object detectors, in order to get pig's bounding boxes. Finally, we merge the bounding boxes between consecutive key frames in order to reduce false positive and negative cases. Based on the experiment results with a video data set obtained from a pig farm, we confirmed that the pigs could be detected with an accuracy of 97% at a processing speed of 37fps.

System Identification Using the Second Order MLMS Algorithm (제2차 MLMS 알고리즘을 이용한 시스템 Identification)

  • 김해정;이두수
    • Journal of the Korean Institute of Telematics and Electronics B
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    • v.29B no.11
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    • pp.8-15
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    • 1992
  • This paper analyzes the properties of such algorithm that corresponds to the LMS algorithm with additional update terms, parameterized by the scalar factors $\alpha$ and $\beta$, and presents its structure. The analysis of convergence leads to complex eigenvalues of the transition matrix for the mean weight vector. Regions in which the algorithm becomes stable are demonstrated. The computational cmomplexities of MLMS algorithms are compared with those of MADF, sign and the conventional LMS algorithms. In application of the system identification the second order momentum MLMS algorithm has faster convergence speed than LMS and the first order MLMS algorithms.

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QUASILINEARIZATION FOR SECOND ORDER SINGULAR BOUNDARY VALUE PROBLEMS WITH SOLUTIONS IN WEIGHTED SPACES

  • Devi, J.Vasundhara;Vatsala, A.S.
    • Journal of the Korean Mathematical Society
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    • v.37 no.5
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    • pp.823-833
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    • 2000
  • In this paper, we develop the method of quasilinearization comvined with the methos of upper and lower solutions for singular second order boundary value problems in weighted spaces. The sequences constructed converge uniformly and monotonically to the unique of the second singular order boundary value problem. Further we prove the rate of convergence is quadratic.

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A SEXTIC-ORDER VARIANT OF DOUBLE-NEWTON METHODS WITH A SIMPLE BIVARIATE WEIGHTING FUNCTION

  • Kim, Young Ik
    • Journal of the Chungcheong Mathematical Society
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    • v.27 no.3
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    • pp.513-521
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    • 2014
  • Via extension of the classical double-Newton method, we propose high-order family of two-point methods in this paper. Theoretical and computational properties of the proposed methods are fully investigated along with a main theorem describing methodology and convergence analysis. Typical numerical examples are thoroughly treated to verify the underlying theory.

A Design of Advanced Distribution Management System Based on IT/OT Convergence (IT/OT Convergence 기반의 Advanced Distribution Management System의 설계)

  • Lim, Il-Hyung;Lee, Seung-Joo;Park, Jong-Ho;Shin, Yong-Hak
    • The Transactions of The Korean Institute of Electrical Engineers
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    • v.65 no.5
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    • pp.753-759
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    • 2016
  • Power automation system to operate power distribution systems can be distinguished by distribution SCADA with remote monitoring and control; and distribution automation system with basic functions such as service restoration to the distribution SCADA; and distribution management system which is operated by various applications in order to enhance distribution system operation performance based on the distribution automation system. In the technological change, a technical boundary of information technology (IT) and operation technology (OT) is being blurred by that new concepts such as interoperability. In addtion, IT/OT convergence has been proposed by the improvement of ICT and power system technology. At the viewpoint, advanced distribution management system (ADMS) to have the new concepts and to increase distribution system operation efficiency through global information and functions from the other systems has been proposed. In order to implement the ADMS, IT and OT have to be employed together on the ADMS; and the concept-based IT/OT convergence concept has been presented. Therefore, this paper introduces ADMS and IT/OT convergence and proposes a design of IT/OT convergence based ADMS system design with configurations and functions.