• Nonlinear Functional Analysis and Applications
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• v.26 no.1
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• pp.1-11
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• 2021

In this paper we study the weak and strong convergence to minimizers of convex function of proximal point algorithm SP-iteration of three multivalued nonexpansive mappings in a Hilbert space.

• Bulletin of the Korean Mathematical Society
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• v.59 no.4
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• pp.1019-1044
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• 2022

In this paper, we propose new algorithms for solving equilibrium and multivalued variational inequality problems in a real Hilbert space. The first algorithm for equilibrium problems uses only one approximate projection at each iteration to generate an iteration sequence converging strongly to a solution of the problem underlining the bifunction is pseudomonotone. On the basis of the proposed algorithm for the equilibrium problems, we introduce a new algorithm for solving multivalued variational inequality problems. Some fundamental experiments are given to illustrate our algorithms as well as to compare them with other algorithms.

• Journal of the Korean Mathematical Society
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• v.55 no.6
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• pp.1529-1540
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• 2018

The matrix equation $X^p+A^*XA=Q$ has been studied to find the positive definite solution in several researches. In this paper, we consider fixed-point iteration and Newton's method for finding the matrix p-th root. From these two considerations, we will use the Newton-Schulz algorithm (N.S.A). We will show the residual relation and the local convergence of the fixed-point iteration. The local convergence guarantees the convergence of N.S.A. We also show numerical experiments and easily check that the N.S. algorithm reduce the CPU-time significantly.

• Smart Structures and Systems
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• v.15 no.1
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• pp.169-189
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• 2015

Convergence difficulty and available complete measurement information have been considered as two primary challenges for the identification of large-scale engineering structures. In this paper, a time domain substructural identification approach by combining a weighted adaptive iteration (WAI) algorithm and an extended Kalman filter method with a weighted global iteration (EFK-WGI) algorithm was proposed for simultaneous identification of physical parameters of concerned substructures and unknown external excitations applied on it with limited response measurements. In the proposed approach, according to the location of the unknown dynamic loadings and the partially available structural response measurements, part of structural parameters of the concerned substructure and the unknown loadings were first identified with the WAI approach. The remaining physical parameters of the concerned substructure were then determined by EFK-WGI basing on the previously identified loadings and substructural parameters. The efficiency and accuracy of the proposed approach was demonstrated via a 20-story shear building structure and 23 degrees of freedom (DOFs) planar truss model with unknown external excitation and limited observations. Results show that the proposed approach is capable of satisfactorily identifying both the substructural parameters and unknown loading within limited iterations when both the excitation and dynamic response are partially unknown.

• Korean Journal of Remote Sensing
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• v.25 no.5
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• pp.455-464
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• 2009

Lee(2009) proposed the boundary-adaptive despeckling method using a Bayesian model which is based on the lognormal distribution for image intensity and a Markov random field(MRF) for image texture. This method employs the Point-Jacobian iteration to obtain a maximum a posteriori(MAP) estimate of despeckled imagery. The boundary-adaptive algorithm is designed to use less information from more distant neighbors as the pixel is closer to boundary. It can reduce the possibility to involve the pixel values of adjacent region with different characteristics. The boundary-adaptive scheme was comprehensively evaluated using simulation data and the effectiveness of boundary adaption was proved in Lee(2009). This study, as an extension of Lee(2009), has suggested a modified iteration algorithm of MAP estimation to enhance computational efficiency and to combine classification. The experiment of simulation data shows that the boundary-adaption results in yielding clear boundary as well as reducing error in classification. The boundary-adaptive scheme has also been applied to high resolution Terra-SAR data acquired from the west coast of Youngjong-do, and the results imply that it can improve analytical accuracy in SAR application.

• Journal of the Korean Operations Research and Management Science Society
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• v.28 no.3
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• pp.61-66
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• 2003

In many multiple regression analyses, the “multi-collinearity” problem arises since some independent variables are highly correlated with each other. Practically, the Ridge regression method is often adopted to deal with the problems resulting from multi-collinearity. We propose a better alternative method using iteration to obtain an exact least squares estimator. We prove the solvability of the proposed algorithm mathematically and then compare our method with the traditional one.

• Proceedings of the KSRS Conference
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• 2003.11a
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• pp.1403-1405
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• 2003

This paper focuses on the image correction under few GCPs, utilizes the collinearity equation, and builds up this mathematics model of space backside resection based on condition adjustment. Then calculates the adjusted elements of exterior orientation by iteration algorithm, and evaluates the precision. And demonstrates the high-precision, affection and wide-supplying-perspective of this model.

• The Journal of Korean Institute of Communications and Information Sciences
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• v.21 no.3
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• pp.564-575
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• 1996

Conventional decoding procedures have some problems in order to obtain reconstructed images with high speed. In this paper, the solutions of these are studied and a new fast decoding algorithm is proposed. The proposed algorithm uses a convergence criterion that is used to reduce the redundant iteration in the conventional method and to determine continuation of decoding. The initical image similar to roiginal image is estimated firstly in this algorithm. From the simulation resuls, the proposed algorithm is able to achieve the reconstructed image within 3-4 iteration under the objective criterion. Without any increment of the memory, the quality of the image reconstructed by the proposed algorithm has same quality asthe conventional method.

• Journal of Korea Multimedia Society
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• v.22 no.9
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• pp.1029-1035
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• 2019

In this paper, a tentative Kth order Goldschmidt floating point number Nth root algorithm for K order convergence rate in one iteration is proposed by applying Taylor series to the Goldschmidt square root algorithm. Using the proposed algorithm, Nth root and Nth inverse root can be computed from iterative multiplications without division. It also predicts the error of the algorithm iteration. It iterates until the predicted error becomes smaller than the specified value. Since the proposed algorithm only performs the multiplications until the error gets smaller than a given value, it can be used to improve the performance of a floating point number Nth root unit.

• The Journal of Korean Institute of Communications and Information Sciences
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• v.25 no.5B
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• pp.830-841
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• 2000

We extend the sue of the method of least square to develop a recursive algorithm for the design of adaptive transversal filters such that, given the least-square estimate of this vector of the filter at iteration n-1, we may compute the updated estimate of this vector at iteration a upon the arrival of new data. We begin the development of the RLS algorithm by reviewing some basic relations that pertain to the method of least squares. Then, by exploiting a relation in matrix algebra known as the matrix inversion lemma, we develop the RLS algorithm. An important feature of the RLS algorithm is that it utilizes information contained in the input data, extending back to the instant of time when the algorithm is initiated. In this paper, we propose new tap weight updated RLS algorithm in adaptive transversal filter with data-recycling buffer structure. We prove that convergence speed of learning curve of RLS algorithm with data-recycling buffer is faster than it of exiting RL algorithm to mean square error versus iteration number. Also the resulting rate of convergence is typically an order of magnitude faster than the simple LMS algorithm. We show that the number of desired sample is portion to increase to converge the specified value from the three dimension simulation result of mean square error according to the degree of channel amplitude distortion and data-recycle buffer number. This improvement of convergence character in performance, is achieved at the (B+1)times of convergence speed of mean square error increase in data recycle buffer number with new proposed RLS algorithm.