• Journal of applied mathematics & informatics
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• v.27 no.5_6
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• pp.1061-1071
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• 2009

For real generalized reflexive matrices R, S, i.e., $R^T$ = R, $R^2$ = I, $S^T$ = S, $S^2$ = I, we say that real matrix X is (R,S)-symmetric, if RXS = X. In this paper, an iterative algorithm is proposed to solve the least-squares problem of matrix equation AXB = C with (R,S)-symmetric X. Furthermore, the optimal approximation solution to given matrix $X_0$ is also derived by this iterative algorithm. Finally, given numerical example and its convergent curve show that this method is feasible and efficient.

• Journal of the Semiconductor & Display Technology
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• v.11 no.2
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• pp.63-69
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• 2012

As decreasing size of chips, the need of wafer level packaging is increased in semi-conductor and display industries. Temperature uniformity is a crucial factor in vacuum soldering process to guarantee quality of bonding between chips and wafer. In this paper, a stepwise iterative algorithm has been suggested to obtain output profile of each heat source. Since this algorithm is based on open-loop stepwise iterative experimental technique, it is easier to implement and cost effective than real time feedback controls. Along with some experiments, it was shown that the suggested algorithm can remarkably improve temperature uniformity of wafer during whole heating process compared with the ordinary manual trial-and error method.

• Nonlinear Functional Analysis and Applications
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• v.29 no.1
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• pp.69-81
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• 2024

In this paper, we provide certain fixed point results for a generalized 𝛼-nonexpansive mapping, as well as a new iterative algorithm called SRJ-iteration for approximating the fixed point of this class of mappings in the setting of CAT(0) spaces. Furthermore, we establish strong and ∆-convergence theorem for generalized 𝛼-nonexpansive mapping in CAT(0) space. Finally, we present a numerical example to illustrate our main result and then display the efficiency of the proposed algorithm compared to different iterative algorithms in the literature. Our results obtained in this paper improve, extend and unify results of Abbas et al. [10], Thakur et al. [22] and Piri et al. [19].

• Transactions of the Korean Society for Noise and Vibration Engineering
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• v.23 no.5
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• pp.438-444
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• 2013

This paper presents the replication of a desired vibration response by iterative learning control (ILC) system for a vibration motion replication actuator. The vibration motion replication actuator has parameter uncertainties including system nonlinearity and joint nonlinearity. Vehicle manufacturers worldwide are increasingly relying on road simulation facilities that put simulated loads and stresses on vehicles and subassemblies in order to reduce development time. Road simulation algorithm is the key point of developing road simulation system. With the rapid progress of digital signal processing technology, more complex control algorithms including iterative learning control can be utilized. In this paper, ILC algorithm was utilized to produce simultaneously the six channels of desired responses using the Stewart platform composed of six linear electro-magnetic actuators with Halbach magnet array. The convergence rate and accuracy showed reasonable results to meet the requirement. It shows that the algorithm is acceptable to replicate multi-channel vibration responses.

• The Journal of Korean Institute of Electromagnetic Engineering and Science
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• v.23 no.4
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• pp.524-532
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• 2012

In this paper, we used MOM-based BIM(Born Iterative Method) algorithm to implement the inverse scattering for the detection of cancer. We adopted two-dimensional breast structure, integral equations and two-dimensional Green's function is solved with MoM(Method of Moment) to analyzing electromagnetic scattering phenomena. In addition, verifying the calculation of developed inverse scattering algorithm and analyzing medical applicability and limitations of the algorithm.

• Journal of Institute of Control, Robotics and Systems
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• v.4 no.3
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• pp.295-300
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• 1998

In this paper, we point out the possibility of the divergence of control input caused by the estimation error of delay-time when general iterative learning algorithms are applied to a class of linear dynamic systems with time-delay in which delay-time is not exactly measurable, and then propose a new type of iterative learning algorithm in order to solve this problem. To resolve the uncertainty of delay-time, we propose an algorithm using holding mechanism which has been used in digital control system and/or discrete-time control system. The control input is held as constant value during the time interval of which size is that of the delay-time uncertainty. The output of the system tracks a given desired trajectory at discrete points which are spaced auording to the size of uncertainty of delay-time with the robust property for estimation error of delay-time. Several numerical examples are given to illustrate the effeciency of the proposed algorithm.

• The Journal of the Acoustical Society of Korea
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• v.40 no.3
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• pp.213-218
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• 2021

It is known that total least-squares method shows better estimation performance than least-squares method when noise is present at the input and output at the same time. When total least squares method is applied to data with time series characteristics, Recursive Total Least Squares (RTS) algorithm has been proposed to improve the real-time performance. However, RTLS has numerical instability in calculating the inverse matrix. In this paper, we propose an algorithm for reducing numerical instability as well as having similar convergence to RTLS. For this algorithm, we propose a new RTLS using Iterative Wiener Filter (IWF). Through the simulation, it is shown that the convergence of the proposed algorithm is similar to that of the RTLS, and the numerical robustness is superior to the RTLS.

• Journal of the Institute of Electronics Engineers of Korea SC
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• v.39 no.2
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• pp.85-94
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• 2002

In this paper, we show that the 2nd-order iterative learning control algorithm with CITE is more effective and has better convergence performance than the algorithm without CITE in the case of the existence of initialization errors, for the trajectory-tracking control of dynamic systems with unidentified parameters. In contrast to other known methods, the proposed learning control scheme utilize more than one past error history contained in the trajectories generated at prior iterations, and a CITE term is added in the learning control scheme for the enhancement of convergence speed and robustness to disturbances and initialization errors. And the convergence proof of the proposed algorithm in the case of the existence of initialization error is given in detail, and the effectiveness of the proposed algorithm is shown by simulation results.

• Journal of applied mathematics & informatics
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• v.26 no.1_2
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• pp.213-222
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• 2008

Iterative methods are often suitable for solving least squares problems min$||Ax-b||_2$, where A $\epsilon\;\mathbb{R}^{m{\times}n}$ is large and sparse. The well known LSQR algorithm is among the iterative methods for solving these problems. A good preconditioner is often needed to speedup the LSQR convergence. In this paper we present the numerical experiments of applying a well known preconditioner for the LSQR algorithm. The preconditioner is based on the $A^T$ A-orthogonalization process which furnishes an incomplete upper-lower factorization of the inverse of the normal matrix $A^T$ A. The main advantage of this preconditioner is that we apply only one of the factors as a right preconditioner for the LSQR algorithm applied to the least squares problem min$||Ax-b||_2$. The preconditioner needs only the sparse matrix-vector product operations and significantly reduces the solution time compared to the unpreconditioned iteration. Finally, some numerical experiments on test matrices from Harwell-Boeing collection are presented to show the robustness and efficiency of this preconditioner.

• The Journal of Korean Institute of Communications and Information Sciences
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• v.32 no.11C
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• pp.1073-1078
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• 2007

In this paper, we propose an iterative mixed norm image restoration algorithm using multi regularization parameters. A functional which combines the regularized $l_2$ norm functional and the regularized $l_4$ norm functional is proposed to efficiently remove arbitrary noise. The smoothness of each functional is determined by the regularization parameters. Also, a regularization parameter is used to determine the relative importance between the regularized $l_2$ norm functional and the regularized $l_4$ norm functional using kurtosis. An iterative algorithm is utilized for obtaining a solution and its convergence is analyzed. Experimental results demonstrate the capability of the proposed algorithm.