• Communications of the Korean Mathematical Society
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• v.37 no.3
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• pp.939-955
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• 2022

In this paper, we study a first-order non-linear singularly perturbed Volterra integro-differential equation (SPVIDE). We discretize the problem by a uniform difference scheme on a Bakhvalov-Shishkin mesh. The scheme is constructed by the method of integral identities with exponential basis functions and integral terms are handled with interpolating quadrature rules with remainder terms. An effective quasi-linearization technique is employed for the algorithm. We establish the error estimates and demonstrate that the scheme on Bakhvalov-Shishkin mesh is O(N^-1) uniformly convergent, where N is the mesh parameter. The numerical results on a couple of examples are also provided to confirm the theoretical analysis.

• Journal of the Korean Mathematical Society
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• v.60 no.2
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• pp.273-302
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• 2023

In this paper, a fully discrete numerical scheme for the viscoelastic Oldroyd flow is considered with an introduced auxiliary variable. Our scheme is based on the finite element approximation for the spatial discretization and the backward Euler scheme for the time discretization. The integral term is discretized by the right trapezoidal rule. Firstly, we present the corresponding equivalent form of the considered model, and show the relationship between the origin problem and its equivalent system in finite element discretization. Secondly, unconditional stability and optimal error estimates of fully discrete numerical solutions in various norms are established. Finally, some numerical results are provided to confirm the established theoretical analysis and show the performances of the considered numerical scheme.

• 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 applied mathematics & informatics
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• v.6 no.1
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• pp.143-162
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• 1999

In this paper we consider the second order generalized difference scheme for the two-point boundary value problem and ob-tain optimal order error estimates in $L^\infty$ and $W^{1,\infty}$ The results in this paper perfect the theory of the second order generalized difference method.

• 제어로봇시스템학회:학술대회논문집
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• 2001.10a
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• pp.56.1-56
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• 2001

Initial attitude error is one of the large error sources in the navigation errors of SDINS. And it is important to decide the initial attitude of SDINS. The method, like a self-alignment or a transfer alignment method, is required to a precise INS. If we do not have a precise INS, we should get large attitude error. After performing the initial alignment, a vehicle has the initial attitude error. Therefore, it results in navigation error due to the initial attitude error. But, if we use position information during flight, we could estimate and compensate a vehicle attitude error. So, we can maintain a precise attitude in spite of existing the initial attitude error. Using the uplinked position information from a land-based radar system, the new algorithm estimates the attitude of the SDINS during flight ...

• The Transactions of The Korean Institute of Electrical Engineers
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• v.60 no.1
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• pp.205-213
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• 2011

The Long Term Evolution (LTE) system is designed to provide a high quality data service for fast moving mobile users. It is based on the Orthogonal Frequency Division Multiplexing (OFDM) and relies its channel estimation on the training samples which are systematically built within the transmitting data. Either a preamble or a lattice type is used for the distribution of training samples and the latter suits better for the multipath fading channel environment whose channel frequency response (CFR) fluctuates rapidly with time. In the lattice-type structure, the estimation of the CFR makes use of the least squares estimate (LSE) for each pilot samples, followed by an interpolation both in time-and in frequency-domain to fill up the channel estimates for subcarriers corresponding to data samples. All interpolation schemes should rely on the pilot estimates only, and thus, their performances are bounded by the quality of pilot estimates. However, the additive noise give rise to high fluctuation on the pilot estimates, especially in a communication environment with low signal-to-noise ratio. These high fluctuations could be monitored in the alternating high values of the first forward differences (FFD) between pilot estimates. In this paper, we analyzed statistically those FFD values and propose a postprocessing algorithm to suppress high fluctuations in the noisy pilot estimates. The proposed method is based on a localized adaptive moving-average filtering. The performance of the proposed technique is verified on a multipath environment suggested on a 3GPP LTE specification. It is shown that the mean-squared error (MSE) between the actual CFR and pilot estimates could be reduced up to 68% from the noisy pilot estimates.

• Proceedings of the Korean Society of Computational and Applied Mathematics Conference
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• 2002.09a
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• pp.17.2-17
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• 2002

• The Korean Journal of Applied Statistics
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• v.24 no.1
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• pp.207-216
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• 2011

Bootstrap is a resampling technique to find an estimate of parameters or to evaluate the estimate. This technique has been used in estimating parameters in linear model(LM) and generalized linear model(GLM). In this paper, we explore the possibility of applying Bootstrapping Residuals, Pairs, and an Estimating Equation that are most widely used in LM and GLM to the generalized estimating equation(GEE) algorithm for modelling repeatedly measured regression data sets. We compared three bootstrapping methods with coefficient and standard error estimates of GEE models from one simulated and one real data set. Overall, the estimates obtained from bootstrap methods are quite comparable, except that estimates from bootstrapping pairs are somewhat different from others. We conjecture that the strange behavior of estimates from bootstrapping pairs comes from the inconsistency of those estimates. However, we need a more thorough simulation study to generalize it since those results are coming from only two small data sets.

• Journal of Institute of Control, Robotics and Systems
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• v.17 no.9
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• pp.947-953
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• 2011

Radome aberration error causes degradation of miss distance as well as stability of high maneuver missile system with RF seeker. A study about radome compensation method is important in this kind of missile system design. Several kinds of methods showed good compensation performance in their paper. Proposed adaptive Particle filter estimates line of sight rate excluding the radome induced error. This paper shows effectiveness of adaptive Particle filter as compensation method of radome aberration error. Robust performance of this filter depends on external aiding measurement, target acceleration. Tuning of system error covariance can make this filter unsensitive against the error of target acceleration information. This paper demonstrates practical usage of adaptive Particle filter for reducing miss distance and increasing stability against disturbance of radome aberration error through performance analysis.

• The Journal of Korean Institute of Communications and Information Sciences
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• v.22 no.8
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• pp.1691-1697
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• 1997

This paper presents a new motion compensated error coding method suitable for region based image coding system. Compared with block based conding, the region based coding improves subjective quality as it estimates and compensates 2D (or 3D) translantional, rotational, and scaling motion for each regions. although the region based coding has this advantage, its merit is reduced as bock-DCT (2D-DCT) is used to encode motion-compensated error. To overcome this problem, a new region adaptive motion compensated error coding technique which improver subjective and objective quality in the region boundary is proposed in this paper. In the proposed method, regions with large error are estimated using contour of the regions and contrast between the regions. The regions estiated as those with large error are coded by arbitrarily shaped image segment coding method. The mask information of the coded regions is not transmitted because it is estimated as the same algorithm in the encoder and the decoder. The proposed region adaptive motion conpensated error coding method improves about 0.5dB when it is compared with conventional block based method.