• 대한수학회보
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• 제49권1호
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• pp.175-195
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• 2012

Representing planar Pythagorean hodograph (PH) curves by the complex roots of their hodographs, we standardize Farouki's double cubic method to become the undetermined junction point (UJP) method, and then prove the generic existence of solutions for general $C^1$ Hermite interpolation problems. We also extend the UJP method to solve $C^2$ Hermite interpolation problems with multiple PH cubics, and also prove the generic existence of solutions which consist of triple PH cubics with $C^1$ junction points. Further generalizing the UJP method, we go on to solve $C^2$ Hermite interpolation problems using two PH quintics with a $C^1$ junction point, and we also show the possibility of applying the modi e UJP method to $G^2[C^1]$ Hermite interpolation.

• 한국국방경영분석학회지
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• 제24권1호
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• pp.146-156
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• 1998

Cholesky factorization is known to be inefficient to problems with dense column and network problems in interior point methods. We use the conjugate gradient method and preconditioners to improve the convergence rate of the conjugate gradient method. Several preconditioners were applied to LPABO 5.1 and the results were compared with those of CPLEX 3.0. The conjugate gradient method shows to be more efficient than Cholesky factorization to problems with dense columns and network problems. The incomplete Cholesky factorization preconditioner shows to be the most efficient among the preconditioners.

• Journal of the Korean Society for Industrial and Applied Mathematics
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• 제7권1호
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• pp.1-5
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• 2003

We suggest Bisection method, Fixed point method and Newton's method for finding the intersection point of a nonparametric surface and a line in $R^3$ and apply ray-tracing in Color Picture Tube or Color Display Tube.

• Journal of the Korean Data and Information Science Society
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• 제15권1호
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• pp.107-117
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• 2004

Change point testing problem is considered. Kernel density estimators are used for constructing proposed change point test statistics. The proposed method can be used to the hypothesis testing of not only parameter change but also distributional change. Bootstrap method is applied to get the sampling distribution of proposed test statistic. Small sample Monte Carlo Simulation were also conducted in order to show the performance of proposed method.

• 대한수학회보
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• 제46권3호
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• pp.521-534
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• 2009

In this paper we present new large-update primal-dual interior point algorithms for $P_*$ linear complementarity problems(LAPS) based on a class of kernel functions, ${\psi}(t)={\frac{t^{p+1}-1}{p+1}}+{\frac{1}{\sigma}}(e^{{\sigma}(1-t)}-1)$, p $\in$ [0, 1], ${\sigma}{\geq}1$. It is the first to use this class of kernel functions in the complexity analysis of interior point method(IPM) for $P_*$ LAPS. We showed that if a strictly feasible starting point is available, then new large-update primal-dual interior point algorithms for $P_*$ LAPS have $O((1+2+\kappa)n^{{\frac{1}{p+1}}}lognlog{\frac{n}{\varepsilon}})$ complexity bound. When p = 1, we have $O((1+2\kappa)\sqrt{n}lognlog\frac{n}{\varepsilon})$ complexity which is so far the best known complexity for large-update methods.

• 한국콘텐츠학회논문지
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• 제18권2호
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• pp.231-239
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• 2018

본 논문은 다중 초기 소실점 후보를 사용해서 소실점을 검출하는 것을 제안한다. 소실점은 3차원 구조복원 등에 사용되는 중요한 기하정보이다. 소실점은 실내 환경의 경우 세 개의 소실점이 검출된다. 기존 초기 소실점을 하나만 검출하는 방식은 가장 높은 투표합의 초기 소실점이 최적의 소실점의 위치와 다를 수 있기에 부정확 할 수 있다. 따라서 여러 개의 초기 소실점 후보 중 가장 좋은 소실점 후보를 채택하는 방식을 사용하면 처음 구해지는 초기 소실점이 적절치 않은 소실점일 경우를 대비할 수 있다. 또한 본 논문에서는 검출된 소실점을 후처리를 통해서 소실점의 위치를 조정하는 방법을 제안한다. 후처리를 통해 기존보다 정확한 소실점을 검출할 수 있다. 실험 결과는 제안하는 방법을 통해 소실점 검출의 정확도가 기존방법보다 약 1~2% 가량 높음을 보여주며, 이에 따라 성능이 향상되었음을 알 수 있다.

• 대한수학회논문집
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• 제25권4호
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• pp.655-669
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• 2010

In this paper we propose new primal-dual interior point methods (IPMs) for $P_*(\kappa)$ linear complementarity problems (LCPs) and analyze the iteration complexity of the algorithm. New search directions and proximity measures are defined based on a class of kernel functions, $\psi(t)=\frac{t^2-1}{2}-{\int}^t_1e{^{q(\frac{1}{\xi}-1)}d{\xi}$, $q\;{\geq}\;1$. If a strictly feasible starting point is available and the parameter $q\;=\;\log\;\(1+a{\sqrt{\frac{2{\tau}+2{\sqrt{2n{\tau}}+{\theta}n}}{1-{\theta}}\)$, where $a\;=\;1\;+\;\frac{1}{\sqrt{1+2{\kappa}}}$, then new large-update primal-dual interior point algorithms have $O((1\;+\;2{\kappa})\sqrt{n}log\;n\;log\;{\frac{n}{\varepsilon}})$ iteration complexity which is the best known result for this method. For small-update methods, we have $O((1\;+\;2{\kappa})q{\sqrt{qn}}log\;{\frac{n}{\varepsilon}})$ iteration complexity.

• International Journal of CAD/CAM
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• 제8권1호
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• pp.45-53
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• 2009

As the point sampling technology evolves rapidly, there has been increasing need in generating tool path from dense point set without creating intermediate models such as triangular meshes or surfaces. In this paper, we present a new tool path generation method from point set using Euclidean distance fields based on Algebraic Point Set Surfaces (APSS). Once an Euclidean distance field from the target shape is obtained, it is fairly easy to generate tool paths. In order to compute the distance from a point in the 3D space to the point set, we locally fit an algebraic sphere using moving least square method (MLS) for accurate and simple calculation. This process is repeated until it converges. The main advantages of our approach are : (1) tool paths are computed directly from point set without making triangular mesh or surfaces and their offsets, and (2) we do not have to worry about no local interference at concave region compared to the other methods using triangular mesh or surface model. Experimental results show that our approach can generate accurate enough tool paths from a point set in a robust manner and efficiently.

• Advances in concrete construction
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• 제16권2호
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• pp.79-89
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• 2023

The occurrence of unexpected horizontal offset in the instrument or target will result in accumulated horizontal deviation in segment alignment with traditional short-line match method. A geometry control method, the four-point method, is developed for precast segmental bridges to avoid the influences of unexpected horizontal offset. The concept of the four-point method is elucidated. Furthermore, the detailed instruments and instructions are introduced. Finally, the four-point method is validated through a practical engineering application. According to the survey data, after short-line match precast construction, the vertical deviations on both sides vary between -5 mm and 5 mm in almost all segments, and the horizontal deviations vary between -4 mm and 4 mm in all segments. Without on-site adjustment, the maximum vertical and horizontal closure gaps are 12.3 and 26.1 mm, respectively. The four-point method is suggested to alleviate the issues associated with relatively poor soil conditions in casting yard.

• Journal of applied mathematics & informatics
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• 제27권3_4호
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• pp.567-579
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• 2009

Recently, Peng et al. proposed a primal-dual interior-point method with new search direction and self-regular proximity for LP. This new large-update method has the currently best theoretical performance with polynomial complexity of O($n^{\frac{q+1}{2q}}\;{\log}\;{\frac{n}{\varepsilon}}$). In this paper we use this search direction to propose a primal-dual interior-point method for convex quadratic programming (QP). We overcome the difficulty in analyzing the complexity of the primal-dual interior-point methods for convex quadratic programming, and obtain the same polynomial complexity of O($n^{\frac{q+1}{2q}}\;{\log}\;{\frac{n}{\varepsilon}}$) for convex quadratic programming.