• The Pure and Applied Mathematics
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• v.17 no.4
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• pp.321-332
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• 2010

In this paper, we experiment image warping and morphing. In image warping, we use radial basis functions : Thin Plate Spline, Multi-quadratic and Gaussian. Then we obtain the fact that Thin Plate Spline interpolation of the displacement with reverse mapping is the efficient means of image warping. Reflecting the result of image warping, we generate two examples of image morphing.

• International Journal of Fuzzy Logic and Intelligent Systems
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• v.13 no.1
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• pp.31-38
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• 2013

Patients with heart disease need long-term monitoring of the electrocardiogram (ECG) signal using a portable electrocardiograph. This trend requires the miniaturization of data storage and faster transmission to medical doctors for diagnosis. The ECG signal needs to be utilized for efficient storage, processing and transmission, and its data must contain the important components for diagnosis, such as the P wave, QRS-complex, and T wave. In this study, we select the vertex which has a larger curvature value than the threshold value for compression. Then, we reconstruct the compressed signal using by radial basis function interpolation. This technique guarantees a lower percentage of root mean square difference with respect to the extracted sample points and preserves all the important features of the ECG signal. Its effectiveness has been demonstrated in the experiment using the Massachusetts Institute of Technology and Boston's Beth Israel Hospital arrhythmia database.

• Journal of applied mathematics & informatics
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• v.14 no.1_2
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• pp.365-376
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• 2004

The purpose of this study is to show that the accuracy of the interpolation method can be at least doubled when additional smoothness requirements and boundary conditions are met. In particular, as a basis function, we are interested in using a conditionally positive definite function $\Phi$ whose generalized Fourier transform is of the form $\Phi(\theta)\;=\;F(\theta)$\mid$\theta$\mid$^{-2m}$ with a bounded function F > 0.

• Journal of the Korean Society for Aeronautical & Space Sciences
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• v.37 no.5
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• pp.433-441
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• 2009

Generally, the events in nature have multi-disciplinary characteristics. To solve this problems, these days loosely coupled methods are widely applied because of advantage of solvers which are already developed and well proved. Those solvers use different mesh system, so transformation and mapping of data are vital in the field of fluid-structure interaction(FSI). In this paper, the interpolation of deformation which is used globally and compactly supported radial basis functions(RBF), and mapping of force which use principle of virtual work are examined for computing time and accuracy to compare ability with simple 3-D problem. As the results, interpolation scheme of compactly supported radial basis functions are useful to interpolation and mapping for large-scale airplane in FSI with a k-dimensional tree(kd-tree) which is a space-partitioning data structure for organizing points in a k-dimensional space.

• 한국전산유체공학회:학술대회논문집
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• 2009.04a
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• pp.121-124
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• 2009

A moving mesh system is one of the critical parts in a computational fluid dynamics analysis. In this study, the RBF(Radial Basis Function) which shows better performance than hybrid meshes was developed to obtain the deformed grid. The RBF method can handle large mesh deformations caused by translations, rotations and deformations, both for 2D and 3D meshes. Another advantage of the method is that it can handle both structured and unstructured grids with ease. The method uses a volume spline technique to compute the deformation of block vertices and block edges, and deformed shape.

• Journal of applied mathematics & informatics
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• v.27 no.5_6
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• pp.1087-1095
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• 2009

In this paper, we study approximation method from scattered data to the derivatives of a function f by a radial basis function $\phi$. For a given function f, we define a nearly interpolating function and discuss its accuracy. In particular, we are interested in using smooth functions $\phi$ which are (conditionally) positive definite. We estimate accuracy of approximation for the Sobolev space while the classical radial basis function interpolation applies to the so-called native space. We observe that our approximant provides spectral convergence order, as the density of the given data is getting smaller.

• Communications of the Korean Mathematical Society
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• v.10 no.4
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• pp.849-854
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• 1995

The interpolation of scattered data with radial basis functions is knwon for its good fitting. But if data get large, the coefficient matrix becomes almost singular. We introduce different knots and nodes to improve condition number of coefficient matrix. The singulaity of new coefficient matrix is investigated here.

• Transactions of the Korean Society of Mechanical Engineers B
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• v.23 no.2
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• pp.243-253
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• 1999

The dual reciprocity boundary element method (DRBEM) is used to solve the Graetz problem of laminar flow inside circular duct. In this method the domain integral tenn of boundary integral equation resulting from source term of governing equation is transformed into equivalent boundary-only integrals by using the radial basis interpolation function, and therefore complicate domain discretization procedure Is completely removed. Velocity profile is obtained by solving the momentum equation first and then, using this velocities as Input data, energy equation Is solved to get the temperature profile by advancing from duct entrance through the axial direction marching scheme. DRBEM solution is tested for the uniform temperature and heat flux boundary condition cases. Local Nusselt number, mixed mean temperature and temperature profile inside duct at each dimensionless axial location are obtained and compared with exact solutions for the accuracy test Solutions arc in good agreement at the entry region as well as fully developed region of circular duct, and their accuracy are verified from error analysis.

• Proceedings of the Korean Institute of Intelligent Systems Conference
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• 1997.11a
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• pp.128-133
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• 1997

This paper examines the relation between multidimensional linear interpolation ( MDI ) and regularization networks, and shows that and MDI is a special form of regularization networks. For this purpose we propose a triangular basis function ( TBF ) network. Also we verified the condition when our proposed TBF becomes a well-known radial basis function ( RBF ).

• Journal of the Korean Society for Industrial and Applied Mathematics
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• v.19 no.4
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• pp.409-416
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• 2015

In many practical applications, we face the problem of reconstruction of an unknown function sampled at some data points. Among infinitely many possible reconstructions, the thin plate spline interpolation is known to be the least oscillatory one in the Beppo-Levi semi norm, when the data points are sampled in $\mathbb{R}^2$. The traditional proofs supporting the argument are quite lengthy and complicated, keeping students and researchers off its understanding. In this article, we introduce a simple and short proof for the optimal reconstruction. Our proof is unique and reguires only elementary mathematical background.