• Journal of applied mathematics & informatics
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• 제26권3_4호
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• pp.445-456
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• 2008

We characterize the helical polynomial space curves and solve the first-order Hermite interpolation problem for helical polynomial space quintics.

• Journal of Electrical Engineering and Technology
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• 제10권2호
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• pp.676-687
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• 2015

Path planning algorithms are used to allow mobile robots to avoid obstacles and find ways from a start point to a target point. The general path planning algorithm focused on constructing of collision free path. However, a high continuous path can make smooth and efficiently movements. To improve the continuity of the path, the searched waypoints are connected by the proposed polynomial interpolation. The existing polynomial interpolation methods connect two points. In this paper, point groups are created with three points. The point groups have each polynomial. Polynomials are made by matching the differential values and simple matrix calculation. Membership functions are used to distribute the weight of each polynomial at overlapped sections. As a result, the path has $G^2$ continuity. In addition, the proposed method can analyze path numerically to obtain curvature and heading angle. Moreover, it does not require complex calculation and databases to save the created path.

• 대한전자공학회논문지SP
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• 제48권3호
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• pp.119-124
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• 2011

보간 필터는 통신과 멀티미디어 응용프로그램에 널리 사용된다. 다항식 보간은 보간된 값을 얻기 위해서 입력정보에 따른 다항식의 계수를 계산한다. 최근에 다항식 보간방법의 성능을 향상시키기 위하여 보조필터를 이용한 FIR 보간방법이 제안되었다. 본 논문에서는 최대값 또는, 최소값 계산 등 특정 순간의 보간 값만 필요한 응용에서 보간필터의 성능을 더욱 향상시킬 수 있는 보조필터를 이용한 가중치 적용 보간방법을 제안한다. 제안한 방법을 X-선 형광분석장치에서 사용되는 정규분포곡선에 대한 보간에 적용하여 기존 보간방법에 비해 더욱 우수한 보간 성능이 제공됨을 보인다.

• Nuclear Engineering and Technology
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• 제31권3호
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• pp.303-313
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• 1999

Various interpolation methods have been compared for reconstruction of LMR pin power distributions in hexagonal geometry. Interpolation functions are derived for several combinations of nodal quantities and various sets of basis functions, and tested against fine mesh calculations. The test results indicate that the interpolation functions based on the sixth degree polynomial are quite accurate, yielding maximum interpolation errors in power densities less than 0.5%, and maximum reconstruction errors less than 2% for driver assemblies and less than 4% for blanket assemblies. The main contribution to the total reconstruction error is made tv the nodal solution errors and the comer point flux errors. For the polynomial interpolations, the basis monomial set needs to be selected such that the highest powers of x and y are as close as possible. It is also found that polynomials higher than the seventh degree are not adequate because of the oscillatory behavior.

• 대한전자공학회논문지SP
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• 제45권4호
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• pp.78-83
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• 2008

보간 필터는 샘플링된 데이터의 사이 값을 추정하는 회로로서 시간 복원 시스템에 널리 사용된다. 다항식 보간은 주어진 점의 정보를 가지고 각 다항식의 계수를 계산하여 추정하는 위치의 값을 계산하는 것이다. 본 논문에서는 Lagrange 3차 보간 방정식에서 주어진 계수를 제안한 ${\delta}$함수로 변환하는 보조 필터를 이용하여 보간 성능을 개선시키는 방법을 제안한다. 예제를 이용하여 제안한 구조와 기존 보간 회로 구조와 비교하였을 때 효율적임을 입증한다.

• KSII Transactions on Internet and Information Systems (TIIS)
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• 제13권7호
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• pp.3690-3713
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• 2019

According to the main group key management schemes logical key hierarchy (LKH), exclusion basis systems (EBS) and other group key schemes are limited in network structure, collusion attack, high energy consumption, and the single point of failure, this paper presents a group key management scheme for wireless sensor networks based on Lagrange interpolation polynomial characteristic (AGKMS). That Chinese remainder theorem is turned into a Lagrange interpolation polynomial based on the function property of Chinese remainder theorem firstly. And then the base station (BS) generates a Lagrange interpolation polynomial function f(x) and turns it to be a mix-function f(x)' based on the key information m(i) of node i. In the end, node i can obtain the group key K by receiving the message f(m(i))' from the cluster head node j. The analysis results of safety performance show that AGKMS has good network security, key independence, anti-capture, low storage cost, low computation cost, and good scalability.

• 대한수학회논문집
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• 제21권2호
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• pp.397-407
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• 2006

We construct polynomial-fitting interpolation rules to agree with a function f and its first derivative f' at equally spaced nodes on the interval of interest by introducing a linear functional with which we produce systems of linear equations. We also introduce a matrix whose determinant is not zero. Such a property makes it possible to solve the linear systems and then leads to a conclusion that the rules are uniquely determined for the nodes. An example is investigated to compare the rules with Hermite interpolating polynomials.

• 대한기계학회논문집
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• 제19권2호
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• pp.433-442
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• 1995

For the line search of a multi-variable optimization, an efficient algorithm is presented. The algorithm sequentially employs several polynomial approximations such as 2-point quadratic interpolation, 3-point cubic interpolation/extrapolation and 4-point cubic interpolation/extrapolation. The order of polynomial function is automatically increased for improving the accuracy of approximation. The method of approximation (interpolation or extrapolation) is automatically switched by checking the slope information of the sample points. Also, for selecting the initial step length along the descent vector, a new approach is presented. The performance of the proposed method is examined by solving typical test problems such as mathematical problems, mechanical design problems and dynamic response problems.

• 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.

• 한국정보통신학회:학술대회논문집
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• 한국해양정보통신학회 2001년도 춘계종합학술대회
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• pp.672-675
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• 2001

본 논문에서 Interpolation Methods를 이용하여 보다 정화한 풍속을 계산하는 방법과 보다 정확한 풍향을 계산하기 위하여 Interpolation Polynomial을 찾는 방법을 제안하였고, 이렇게 제안된 방법을 이용하여 3-Cup Anemometer의 성능을 개선하였다. 우리는 풍향, 풍속의 관측을 위해 기구부는 3-cup Type Anemometer로, 전자부는 Photo Sensor를 이용하여 구현하였다. 정확한 풍속과 풍향의 측정을 위해서는 시스템의 메모리 한계 및 성능을 고려한 시스템 설계와 8비트 Gray Code Film으로 256(= 2$^{8}$ )개의 각도 Data로 360$^{\circ}$를 표현하는 방법이다.