• 대한수학회지
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• 제42권2호
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• pp.305-334
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• 2005

The objective of this study is to analyze the decay characteristics of the hat interpolation wavelet coefficients of some smooth functions defined in a two-dimensional space. The motivation of this research is to establish some fundamental mathematical foundations needed in justifying the adaptive multiresolution analysis of the hat-interpolation wavelet-Galerkin method. Though the hat-interpolation wavelet-Galerkin method has been successful in some classes of problems, no complete error analysis has been given yet. As an effort towards this direction, we give estimates on the decaying ratios of the wavelet coefficients at children interpolation points to the wavelet coefficient at the parent interpolation point. We also give an estimate for the difference between non-adaptively and adaptively interpolated representations.

• 대한전기학회논문지:시스템및제어부문D
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• 제51권6호
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• pp.235-240
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• 2002

This paper presents a new method for estimating the block pulse series coefficients by using the Lagrange's second order interpolation polynomial. Block pulse functions have been used in a variety of fields such as the analysis and controller design of the systems. When the block pulse functions are used, it is necessary to find the more exact value of the block pulse series coefficients. But these coefficients have been estimated by the mean of the adjacent discrete values, and the result is not sufficient when the values are changing extremely. In this paper, the method for improving the accuracy of the block pulse series coefficients by using the Lagrange's second order interpolation polynomial is presented.

• 한국지진공학회논문집
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• 제11권1호
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• pp.59-65
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• 2007

IBC와 KBC의 지반분류는 ft-kips 단위체계를 기본으로 하고, 지반종류를 단일 지반특성값이 아닌 지반특성값 범위로 규정하여 지반종류에 따른 전단파속도와 지반계수들 간의 불명확한 관계 때문에 지반계수의 선형보간이 쉽지 않다. 또한, KBC의 지반분류에서 각 지반종류에 대한 지반특성값 범위가 너무 넓어서 구조기술자들이 다양한 지반의 실제적인 지반계수를 추정하는데 어려움을 격고 있다. 이 연구에서는 SI 단위체계를 고려한 새로운 지반분류체계를KBC등 차세대 내진설계기준을 위해 제안하였고, 제안된 새로운 지반분류에 따라 지반계수들의 선형보간 가능성을 검토하기 위해 $F_{a},\;F_{v}$, 지반계수들의 비교에 관한 연구를 수행하였다. 연구결과에 의하면, SI 단위체계와 얕게 묻힌기초 밑 30m 지반의 지반특성을 고려한 새로 제안한 지반분류체계를 이용하는 것이 지반계수의 선형보간을 위해서 보다 합리적이고, 설계스펙트럼 가속도계수의 선형보간도 각 지반을 대표하는 전단파속도에 따라 지반계수를 규정함으로써 보다 합리적으로 수행할 수 있다. 연구결과에 따라 KBC 내진설계기준을 위한 새로운 지반분류체계와 선형보간이 가능한 설계스펙트럼 가속도 계수를 제안하였다.

• 대한수학회논문집
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• 제37권1호
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• pp.303-326
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• 2022

Our aim is to construct Hermite-type exponentially fitted interpolation formulas that use not only the pointwise values of an 𝜔-dependent function f but also the values of its first derivative at three unequally spaced nodes. The function f is of the form, f(x) = g₁(x) cos(𝜔x) + g₂(x) sin(𝜔x), x ∈ [a, b], where g₁ and g₂ are smooth enough to be well approximated by polynomials. To achieve such an aim, we first present Hermite-type exponentially fitted interpolation formulas I_N built on the foundation using N unequally spaced nodes. Then the coefficients of I_N are determined by solving a linear system, and some of the properties of these coefficients are obtained. When N is 2 or 3, some results are obtained with respect to the determinant of the coefficient matrix of the linear system which is associated with I_N. For N = 3, the errors for I_N are approached theoretically and they are compared numerically with the errors for other interpolation formulas.

• 항공우주기술
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• 제11권1호
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• pp.98-102
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• 2012

비냉각형 열상 시스템에 대한 관심이 국방 및 항공우주 분야에서 증가하고 있다. 특히, 국방분야 무기체계에서는 무인화 및 주야간 적군 탐지를 위한 요소기술로 활용되고 있다. 비냉각형 열상 시스템의 연구 분야 중 저비용, 저전력, 소형화를 위한 비냉각형 TEC(Thermal Electric Cooler)-less 열상 시스템에 대한 연구가 활발히 진행되고 있다. 그러나 TEC-less로 운영하기 위해서는 최적화된 불균일보정 계수의 추출 및 적용이 요구된다. 본 논문에서는 TEC-less로 최적화 된 보정 계수 획득 방법으로 선형 보간법을 이용한 보정 계수 추정 방법인 DCCE-LI(Dynamic Calibration Coefficient Estimation with Linear Interpolation)을 제안하고, 실험을 통해 제안 기법이 기존의 정적 보정 계수를 적용한 것에 비해 IR 영상 품질이 우수하고, 실시간 보정 계수 추정이 가능함을 보인다.

• 대한전기학회논문지:시스템및제어부문D
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• 제52권6호
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• pp.351-358
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• 2003

This paper presents a new method for finding the Block Pulse series coefficients, deriving the Block Pulse integration operational matrices and generalizing the integration operational matrices which are necessary for the control fields using the Block Pulse functions. In order to apply the Block Pulse function technique to the problems of state estimation or parameter identification more efficiently, it is necessary to find the more exact value of the Block Pulse series coefficients and integral operational matrices. This paper presents the method for improving the accuracy of the Block Pulse series coefficients and derives the related integration operational matrices and generalized integration operational matrix by using the Lagrange second order interpolation polynomial.

• 대한전기학회:학술대회논문집
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• 대한전기학회 2003년도 학술대회 논문집 전문대학교육위원
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• pp.55-57
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• 2003

This paper presents a new method for finding the Block Pulse series coefficients and deriving the Block Pulse integration operational matrices which are necessary for the control fields using the Block Pulse functions. In this paper, the accuracy of the Block Pulse series coefficients derived by using the Lagrange second order interpolation polynomial is approved by the mathematical method.

• Journal of the Korean Society for Industrial and Applied Mathematics
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• 제1권1호
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• pp.75-82
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• 1997

An algorithm for computing the cubic spline interpolation coefficients for polynomials is presented in this paper. The matrix equation involved is solved analytically so that numerical inversion of the coefficient matrix is not required. For $f(t)=t^m$, a set of constants along with the degree of polynomial m are used to compute the coefficients so that they satisfy the interpolation constraints but not necessarily the derivative constraints. Then, another matrix equation is solved analytically to take care of the derivative constraints. The results are combined linearly to obtain the unique solution of the original matrix equation. This algorithm is tested and verified numerically for various examples.

• 대한전기학회논문지:시스템및제어부문D
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• 제51권7호
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• pp.286-293
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• 2002

This paper presents a new method for finding the Block Pulse series coefficients and deriving the Block Pulse integration operational matrices which are necessary for the control fields using the Block Pulse functions. In order to apply the Block Pulse function technique to the problems of continuous-time dynamic systems more efficiently, it is necessary to find the more exact value of the Block Pulse series coefficients and drives the related integration operational matrices by using the Lagrange second order interpolation polynomial.

• 전자공학회논문지S
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• 제35S권1호
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• pp.130-140
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• 1998

This paper presents a method to estimate subpixel accuracy motion vectors using a mathermatical model withoug interpolation. the proposed method decides the coefficients of mathematical model, which represents the motion vector which is achieved by full search. And then the proposed method estimates subpixel accuracy motion vector from achieved mathematical model. Step by step mathematical models such as type 1, type 2, type 3, modified bype 2, modified type 3, and Partial Interpolation type 3 are presented. In type 1, quadratic polynomial, which has 9 unknown coefficients and models the 3by 3 pixel plane, is used to get the subpixel accuracy motion vectors by inverse matrix solution. In type 2 and 3, each quadratic polynomial which is simplified from type 1 has 5 and 6 unknown coefficients and is used by least square solution. Modified type 2 and modified type 3 are enhanced models by weighting only 5 pixels out of 9. P.I. type 3 is more accurate method by partial interpolation around subpixel which isachieved by type 3. LThese simulation results show that the more delicate model has the better performance and modified models which are simplified have excellent performance with reduced computational complexity.