• Journal of applied mathematics & informatics
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• v.16 no.1_2
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• pp.1-17
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• 2004

The famous Newton-Kantorovich hypothesis has been used for a long time as a sufficient condition for the convergence of Newton method to a solution of an equation in connection with the Lipschitz continuity of the Frechet-derivative of the operator involved. Using Lipschitz and center-Lipschitz conditions we show that the Newton-Kantorovich hypothesis is weakened. The error bounds obtained under our semilocal convergence result are finer and the information on the location of the solution more precise than the corresponding ones given by the dominating Newton-Kantorovich theorem, and under the same hypotheses/computational cost, since the evaluation of the Lipschitz also requires the evaluation of the center-Lipschitz constant. In the case of local convergence we obtain a larger convergence radius than before. This observation is important in computational mathematics and can be used in connection to projection methods and in the construction of optimum mesh independence refinement strategies.

• Proceedings of the Korean Society of Broadcast Engineers Conference
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• 1997.06a
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• pp.107-112
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• 1997

This paper proposes the regularized constrained iterative image restoration algorithms which apply new space-adaptive methods to degraded image signals, and analyzes the convergence condition of the proposed algorithm. First, we introduce space-adaptive regularization operators which change according to edge characteristics of local images in order to effectively prevent the restored edges and boundaries from reblurring. And, pseudo projection operator is used to reduce the ringing artifact which results from extensive amplification of noise components in the restoration process. The analysed algorithm is stable convergent to the fixed point. According to the experimental results for various signal-to-noise ratios(SNR) and blur models, the proposed algorithms other methods and is robust to noise effects and edge reblurring by regularization especially.

• Transactions of the Korean Society of Automotive Engineers
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• v.3 no.6
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• pp.145-153
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• 1995

An algorithm for the automatic generation of quadrilateral shell elements on three-dimensional sculptured surfaces has been developed, which is one of the key issues in the finite element analysis of structures with complex shapes such as automobile structures. Mesh generation on sculptured surfaces is performed in three steps. First a sculptured surface is transformed to a projection plane, on which the loops are subdivided into subloops by using the best split lines, and with the use of 6-node/8-node loop operators and a layer operator, quadrilateral finite elements are constructed on this plane. Finally, the constructed mesh is transformed back to the original sculptured surfaces. The proposed mesh generation scheme is suited for the generation of non-uniform meshes so that it can be effectively used when the desired mesh density is available. Sample meshes are presented to demonstrate the versatility of the algorithm.

• Journal of the Chungcheong Mathematical Society
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• v.21 no.2
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• pp.269-278
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• 2008

Let ${\partial}D$ be the boundary of the open unit disk D in the complex plane and $L^p({\partial}D)$ the class of all complex, Lebesgue measurable function f for which $\{\frac{1}{2\pi}{\int}_{-\pi}^{\pi}{\mid}f(\theta){\mid}^pd\theta\}^{1/p}<{\infty}$. Let P be the orthogonal projection from $L^p({\partial}D)$ onto ${\cap}_{n<0}$ ker $a_n$. For $f{\in}L^1({\partial}D)$, ${\hat{f}}(z)=\frac{1}{2\pi}{\int}_{-\pi}^{\pi}P_r(t-\theta)f(\theta)d{\theta}$ is the harmonic extension of f. Let ${\hat{P}}$ be the composition of P with the harmonic extension. In this paper, we will show that if $1, then ${\hat{P}}:L^p({\partial}D){\rightarrow}H^p(D)$ is bounded. In particular, we will show that ${\hat{P}}$ is unbounded on $L^{\infty}({\partial}D)$.

• Nuclear Engineering and Technology
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• v.54 no.4
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• pp.1195-1205
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• 2022

Recent developments on spectral diffusion algorithms, i.e., algorithms which exploit the projection of the solution on the eigenfunctions of the Laplacian operator, demonstrated their effective applicability in fast transient conditions. Nevertheless, the numerical error introduced by these algorithms, together with the uncertainties associated with model parameters, may impact the reliability of the predictions on short-lived volatile fission product release from nuclear fuel. In this work, we provide an upper bound on the numerical error introduced by the presented spectral diffusion algorithm, in both constant and time-varying conditions, depending on the number of modes and on the time discretization. The definition of this upper bound allows introducing a methodology to a priori bound the numerical error on short-lived volatile fission product retention.

• The Journal of Korean Institute of Communications and Information Sciences
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• v.33 no.8C
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• pp.583-590
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• 2008

In this paper, we present a spatially adaptive post-processing algorithm for H.264 video coding standard to remove blocking artifacts. The loop filter of H.264 increases computational complexity of the encoder. Furthermore it doesn't clearly remove the blocking artifacts, resulting in over-blurring. For overcoming them, we combine the projection method with the Constraint Least Squares(CLS) method to restore the high quality image. To reflect the Human Visual System, we adopt the weight norm CLS method. Particularly pixel location-based local variance and laplacian operator are newly defined for the CLS method. In addition, the fact that correlation among adjoining pixels is high is utilized to constrain the solution space when the projection method is applied. Quantization Index(QP) of H.264 is also used to control the degree of smoothness. The simulation results show that the proposed post-processing filter works better than the loop filter of H.264 and converges more quickly than the CLS method.

• Journal of Korean Society of Transportation
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• v.27 no.6
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• pp.147-156
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• 2009

We present a methodology for modeling and solving the transit frequency design problem with variable demand. The problem is described as a bi-level model based on a non-cooperative Stackelberg game. The upper-level operator problem is formulated as a non-linear optimization model to minimize net cost, which includes operating cost, travel cost and revenue, with fleet size and frequency constraints. The lower-level user problem is formulated as a capacity-constrained stochastic user equilibrium assignment model with variable demand, considering transfer delay between transit lines. An efficient algorithm is also presented for solving the proposed model. The upper-level model is solved by a gradient projection method, and the lower-level model is solved by an existing iterative balancing method. An application of the proposed model and algorithm is presented using a small test network. The results of this application show that the proposed algorithm converges well to an optimal point. The methodology of this study is expected to contribute to form a theoretical basis for diagnosing the problems of current transit systems and for improving its operational efficiency to increase the demand as well as the level of service.

• Journal of the Korean Institute of Intelligent Systems
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• v.22 no.1
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• pp.87-93
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• 2012

In this paper, we proposed a faulty pattern detection algorithm of TCP(Tape Carrier Package)/COF(Chip On Film), and implemented a real-time system for inspecting TCP/COF. Since TCP/COF has very high resolution having several micro meters, the human operator should visually inspect all the parts through microscope. In this work, we implement an inspection system to detect the faulty pattern, so the operator can visually inspect only the designated parts by the inspection system through the monitor. The proposed defects detection algorithm for TCP/COF packages is implemented by the pattern matching method based on subtracting the reference image from test image. To evaluate performance of the proposal system. we made various experiments according to type of CCD camera and light source as well as illumination projection method. From experimental results, it is confirmed that the proposed system makes it possible to detect effectively the defective TCP/COF film.

• Convergence Security Journal
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• v.7 no.1
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• pp.1-10
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• 2007

Surveillance system with the fixed field of view generally has an identical background and is easy to extract and segment a moving object. However, it is difficult to extract the object when the gray level of the background is varied due to illumination condition in the real circumstance. In this paper we propose the segmentation algorithm to extract effectively the object in spite of the illumination change. In order to minimize the effect of illumination, the proposed algorithm is composed of three modes according to the background generation and the illuminational change. Then the object is finally obtained by using projection and the morphological operator in post-processing. A good segmentation performance is demonstrated by the simulation result.

• Nonlinear Functional Analysis and Applications
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• v.29 no.1
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• pp.131-164
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• 2024

In this research, we study a modified relaxed Tseng method with a single projection approach for solving common solution to a fixed point problem involving finite family of τ-demimetric operators and a quasi-monotone variational inequalities in real Hilbert spaces with alternating inertial extrapolation steps and adaptive non-monotonic step sizes. Under some appropriate conditions that are imposed on the parameters, the weak and linear convergence results of the proposed iterative scheme are established. Furthermore, we present some numerical examples and application of our proposed methods in comparison with other existing iterative methods. In order to show the practical applicability of our method to real word problems, we show that our algorithm has better restoration efficiency than many well known methods in image restoration problem. Our proposed iterative method generalizes and extends many existing methods in the literature.