• Journal of the Korean Mathematical Society
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• v.47 no.6
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• pp.1299-1316
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• 2010

We derive estimates for the truncation, amplitude and jitter type errors associated with Hermite-type interpolations at equidistant nodes of functions in Paley-Wiener spaces. We give pointwise and uniform estimates. Some examples and comparisons which indicate that applying Hermite interpolations would improve the methods that use the classical sampling theorem are given.

• Journal of the Korean Society for Precision Engineering
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• v.17 no.1
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• pp.192-197
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• 2000

In CNC machining, a free curve is cut into small linear segments using the linear interpolation(G01) method. Therefore, the interpolation error along the curve is not constant due to the changing curvature. This paper presents a NURBS (Non-Uniform Rational B-Spline) interpolation algorithm for machining free curves with high precision and high speed. The proposed NURBS interpolation defines the tool path with NURBS parameters and limits the interpolation error to any desired level by adjusting the feed rate considering the curvature of the shape and sampling time. Both linear and NURBS interpolations are compared to show the validity of the proposed algorithm.

• 한국가시화정보학회:학술대회논문집
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• 2004.12a
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• pp.47-55
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• 2004

Several interpolations for image deformation in PIV were evaluated. The tested interpolation methods are linear, quadratic, truncated sinc, windowed sinc, cubic, Lagrange, Gaussian $2^{nd}\;and\;6^{th}$ interpolators. Bias errors and random errors were evaluated in the range of $0\~3.0$ pixel uniform displacement using synthetic images. We also measured the time cost of each interpolator with respect to kernel size. The cubic interpolator with $6\times6$ kernel showed the best results in terms of the performance and time cost.

• Journal of the Optical Society of Korea
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• v.15 no.2
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• pp.168-173
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• 2011

Based on the distinctive characteristics observed in the intensity transmittance of an IPS-LC panel, the previous one-dimensional model is greatly reduced such that only a few data points and their interpolations predict the intensity transmittance of an IPS-LCD with a small error for arbitrary gray levels. Experimental procedure and numerical methods are described in detail.

• Kyungpook Mathematical Journal
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• v.57 no.2
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• pp.287-299
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• 2017

In this paper, we develop an enhanced Chebyshev collocation method based on an integration scheme of the generalized Chebyshev interpolations for solving stiff initial value problems. Unlike the former error embedded Chebyshev collocation method (CCM), the enhanced scheme calculates the solution and its truncation error based on the interpolation of the derivative of the true solution and its integration. In terms of concrete convergence and stability analysis, the constructed algorithm turns out to have the $7^{th}$ convergence order and the A-stability without any loss of advantages for CCM. Throughout a numerical result, we assess the proposed method is numerically more efficient compared to existing methods.

• Journal of Institute of Control, Robotics and Systems
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• v.3 no.1
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• pp.32-39
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• 1997

One of the most important performance criteria in tuning the gain of position loop controller for CNC machining center is the contour error. In this papre we analyze contour error in the linear and circular interpolations for the axis-matched and mismatched cases. To have small contour errors, it is necessary to set the P gain for each axis to be same. And the D gain should be much smaller than the P gain. Baded on the analysis in the frequency domain, we propose a gain tuning method for the P and PD controllers. We show that the PD controller is better than the P controller. The effectiveness of this method is demonstrated by experiments.

• Wind and Structures
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• v.5 no.2_3_4
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• pp.301-316
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• 2002

An important goal of computational wind engineering is to impact the design process with simulations of flow around buildings and bridges. One challenging aspect of this goal is to solve the Navier-Stokes (NS) equations accurately. For the unsteady computations, an adaptive finite element technique may reduce the computer time and storage. The preliminary application of a p-version as well as an h-version adaptive technique to computational wind engineering has been reported in previous paper. The details on the implementation of p-adaptive technique will be discussed in this paper. In this technique, two posteriori error estimations, which are based on the velocity and vorticity, are first presented. Then, the polynomial order of the interpolation function is increased continuously element by element until the estimated error is less than the accepted. The second through sixth orders of hierarchical functions are used as the interpolation polynomials. Unequal order interpolations are used for velocity and pressure. Using the flow around a circular cylinder with Reynolds number of 1000 the two error estimators are compared. The result show that the estimated error based on the velocity is lower than that based on the vorticity.

• Journal of Broadcast Engineering
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• v.18 no.4
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• pp.619-630
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• 2013

In this paper, we propose an edge directed color demosaicing algorithm considering color channel correlation. The proposed method consists of local region classification step and edge directional interpolation step. In the first step, each region of a given Bayer image is classified as normal edge, pattern edge, and flat regions by using intra channel and inter channel gradients. Especially, two criteria and verification process for the normal edge and pattern edge classification are used to reduce edge direction estimation error, respectively. In the second step, edge directional interpolation process is performed according to characteristics of the classified regions. For horizontal and vertical directional interpolations, missing color components are obtained from interpolation equations based on intra channel and inter channel correlations in order to improve the performance of the directional interpolations. The simulation results show that the proposed algorithm outperforms conventional approaches in both objective and subjective terms.

• Nuclear Engineering and Technology
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• v.31 no.3
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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.

• Journal of the Korean Institute of Telematics and Electronics D
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• v.34D no.5
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• pp.67-74
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• 1997

In this paper, we psresent a new scheme to synthetically generate a HPO digital hologram for a three-dimensional image that is modelled as the horizontally stacked two-dimensional images. The proposed method transforms a lightwave field into the angular spectrum of planewaves, which enables this method to use FFT routines, rather than using numerous arithmetic calculations. Hence, this method may be able to not only lead to the dramatically less computation but provide relatively excellent performances due to the phase error-free transformation. We present sampling constraints and implementaton procedure to obtian a hololine for each image and also point out the necessity of interpolation. Simulatioj results are presented to show the comparison with the conventional method in terms of computation time and performances, including the behaviors resulting form the different selection of parameter values to be used in the interpolations.