• Journal of the Korean Mathematical Society
• /
• v.41 no.3
• /
• pp.423-433
• /
• 2004

In this paper we obtained the following: Let H. be a Hilbert space and (equation omitted) be a subspace lattice on H. Let X and Y be operators acting on H. If the range of X is dense in H, then the following are equivalent: (1) there exists an operator A in Alg(equation omitted) such that AX = Y, (2) sup (equation omitted) Moreover, if condition (2) holds, we may choose the operator A such that ∥A∥ = K.

• Proceedings of the Computational Structural Engineering Institute Conference
• /
• 1991.04a
• /
• pp.15-19
• /
• 1991

An attempt has been made to generate a cured boundary by using a transfinite interpolation technique. In the following sections, it will be shown how to construct transfinite interpolants both in h-version and in p-version over polygonal and nonpolygonal regions. Numerirical test cases validate the applicability and superior capability with the help of several structural problem.

• Journal of applied mathematics & informatics
• /
• v.18 no.1_2
• /
• pp.513-524
• /
• 2005

Given operators X and Y acting on a Hilbert space H, an interpolating operator is a bounded operator A such that AX = Y. Let L be a subspace lattice on H. We obtained a necessary and sufficient condition for the existence of an interpolating operator A which is in AlgL.

• The Journal of Korean Institute of Communications and Information Sciences
• /
• v.34 no.4C
• /
• pp.363-370
• /
• 2009

Image interpolation addresses the problem of generating a high-resolution image from its low-resolution version. Classical linear interpolation algorithms are simple and popular, but they produce interpolated image with blurred edges and annoying artifacts, Thus, many edge-based interpolation algorithms have been proposed to improve the subjective quality of the interpolated image, especially around edges on the image. In this paper, we propose a new interpolation algorithm which uses edges extracted from binary image. The proposed algorithm is applied to the image after interpolating using 6-Tap FIR filter. The values of interpolation pixels on edges extracted from binary image are modified using neighborhood pixels on the same edge. Experimental results for various images show that the proposed method provides better performance than existing methods.

• Geophysics and Geophysical Exploration
• /
• v.17 no.2
• /
• pp.88-94
• /
• 2014

Due to mechanical failure or geographical accessibility, the seismic data can be partially missed. In addition, it can be coarsely sampled such as crossline of the marine streamer data. This seismic data that irregular sampled and spatial aliased may cause problems during seismic data processing. Accurate and efficient interpolation method can solve this problem. Futhermore, interpolation can save the acquisition cost and time by reducing the number of shots and receivers. Among various interpolation methods, the Matching Pursuit method can be applied to any sampling type which is regular or irregular. However, in case of using sinusoidal basis function, this method has a limitation in spatial aliasing. Therefore, in this study, we have developed wavelet based Matching Pursuit method that uses wavelet instead of sinusoidal function for the improvement of dealiasing performance. In addition, we have improved interpolation speed by using inner product instead of L-2 norm.

• Journal of the Korea Institute of Information and Communication Engineering
• /
• v.18 no.3
• /
• pp.706-712
• /
• 2014

This paper describes a determining method of weighting factors for two-point interpolation filters. The interpolation filters is implemented by applying modifying functions to the linear interpolation. Here, there is a problem of determining weights when modifying functions being engaged. The previous method determined the weights by imposing c1-continuity on the interpolation kernels. However, this approach is unable to use the property of individual modifying functions. In this paper, on the basis of spectral analyses of the modifying functions and image signals, we provide a determination method by experimental results. Thus, many experiments are carried out to do so. The results indicate that different weights are required for different modifying functions and also the proposed method outperforms than the previous method.

• Journal of the Korean Statistical Society
• /
• v.30 no.2
• /
• pp.231-246
• /
• 2001

Local linear smoothing enjoys several excellent theoretical and numerical properties, an in a range of applications is the method most frequently chosen for fitting curves to noisy data. Nevertheless, it suffers numerical problems in places where the distribution of design points(often called predictors, or explanatory variables) is spares. In the case of univariate design, several remedies have been proposed for overcoming this problem, of which one involves adding additional ″pseudo″ design points in places where the orignal design points were too widely separated. This approach is particularly well suited to treating sparse bivariate design problem, and in fact attractive, elegant geometric analogues of unvariate imputation and interpolation rules are appropriate for that case. In the present paper we introduce and develop pseudo dta rules for bivariate design, and apply them to real data.

• Proceedings of the KIEE Conference
• /
• 2004.07d
• /
• pp.2528-2530
• /
• 2004

Neural network minimization problems are often conditioned and in this contribution way to handle this will be discussed. It is shown that a better conditioned minimization problem can be obtained if the problem is separated with respect to the linear parameters. This will increase the convergence speed of the minimization. One of the most powerful uses of neural networks is in function approximation(curve fitting)[1]. A main characteristic of this solution is that function (f) to be approximated is given not explicitly but implicitly through a set of input-output pairs, named as training set, that can be easily obtained from calibration data of the measurement system. In this context, the usage of Neural Network(NN) techniques for modeling the systems behavior can provide lower interpolation errors when compared with classical methods like polynomial interpolation. This paper solve of single-variable minimization using neural network.

• Journal of the Korean Institute of Telematics and Electronics B
• /
• v.29B no.3
• /
• pp.16-24
• /
• 1992

In this paper, we solve the problem of designing a robust optimal controller which minimizes the H$\infty$-norm of the mixed sensitivity function matrix for linear multivariable systems. For a given minimized value, ${\gamma}$>o, an algorithm of finding all stabilizing controllers, such that the H$\infty$-norm of the mixed sensitivity function matrix is less than ${\gamma}$, is developed. The proposed algorithm, which is based on the model-matching and the interpolation theory, can be used for the H$\infty$-optimization problem.

• Journal of Institute of Control, Robotics and Systems
• /
• v.11 no.9
• /
• pp.755-760
• /
• 2005

This paper proposes an improved implementation algorithm for the continuous-time receding horizon control (RHC). The proposed algorithm has a feature that it has better control performance than the existing algorithm. Main idea of the proposed algorithm is that we can approximate the original RHC problem better by assuming the predicted input trajectory on the prediction horizon has a continuous form, which is constructed from linear interpolation of finite number of vectors. This, in turn, leads to improved control performance. We derive a predictor such that it takes linear interpolation into account and proposes the method by which we can express the cost exactly. Through simulation study fur an inverted pendulum, we illustrate that the proposed algorithm has the better control performance than the existing one.