• Journal of applied mathematics & informatics
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• v.5 no.1
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• pp.23-40
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• 1998

Mixed finite element method is developed to approxi-mate the solution of the initial-boundary value problem for a strongly nonlinear second-order hyperbolic equation in divergence form. Exis-tence and uniqueness of the approximation are proved and optimal-order $L\infty$-in-time $L^2$-in-space a priori error estimates are derived for both the scalar and vector functions approximated by the method.

• Journal of applied mathematics & informatics
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• v.27 no.5_6
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• pp.1221-1234
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• 2009

In this paper, we construct fully discrete discontinuous Galerkin approximations to the solution of linear Sobolev equations. We apply a symmetric interior penalty method which has an interior penalty term to compensate the continuity on the edges of interelements. The optimal convergence of the fully discrete discontinuous Galerkin approximations in ${\ell}^{\infty}(L^2)$ norm is proved.

• Journal of applied mathematics & informatics
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• v.28 no.3_4
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• pp.953-966
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• 2010

In this paper, we develop discontinuous Galerkin methods with penalty terms, namaly symmetric interior penalty Galerkin methods to solve nonlinear parabolic equations. By introducing an appropriate projection of u onto finite element spaces, we prove the optimal convergence of the fully discrete discontinuous Galerkin approximations in ${\ell}^2(L^2)$ normed space.

• Journal of Institute of Control, Robotics and Systems
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• v.17 no.12
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• pp.1183-1187
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• 2011

In this paper, an optimal FIR (Finite-Impulse-Response) filter is proposed for discrete time-varying state-space models. The proposed filter estimates the current state using measured output samples on the recent time horizon so that the variance of the estimation error is minimized. It is designed to be linear, unbiased, with an FIR structure, and is independent of any state information. Due to its FIR structure, the proposed filter is believed to be robust for modeling uncertainty or numerical errors than other IIR filters, such as the Kalman filter. For a general system with system and measurement noise, the proposed filter is derived without any artificial assumptions such as the nonsingular assumption of the system matrix A and any infinite covariance of the initial state. A numerical example show that the proposed FIR filter has better performance than the Kalman filter based on the IIR (Infinite- Impulse-Response) structure when modeling uncertainties exist.

• Proceedings of the KIEE Conference
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• 1997.07b
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• pp.705-707
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• 1997

An optimal tuning algorithm of scaling factors is presented in this paper to automatically improve the performance of fuzzy controller. Especially, fuzzy controller has determined an moderate Scaling factor through trial and error. The presented method estimates automatically the optimal values of I/O scaling factors, using modified steepest descent method and this optimal tuning is for nonlinear input/output scaling factors. Simulation results verify the validity of the presented method.

• Communications of the Korean Mathematical Society
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• v.33 no.2
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• pp.677-693
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• 2018

In this work, we generalize a family of optimal eighth order weighted-Newton methods to Banach spaces and study its local convergence to approximate a locally-unique solution of a system of nonlinear equations. The convergence in this study is shown under hypotheses only on the first derivative. Our analysis avoids the usual Taylor expansions requiring higher order derivatives but uses generalized Lipschitz-type conditions only on the first derivative. Moreover, our new approach provides computable radius of convergence as well as error bounds on the distances involved and estimates on the uniqueness of the solution based on some functions appearing in these generalized conditions. Such estimates are not provided in the approaches using Taylor expansions of higher order derivatives which may not exist or may be very expensive or impossible to compute. The convergence order is computed using computational order of convergence or approximate computational order of convergence which do not require usage of higher derivatives. This technique can be applied to any iterative method using Taylor expansions involving high order derivatives. The study of the local convergence based on Lipschitz constants is important because it provides the degree of difficulty for choosing initial points. In this sense the applicability of the method is expanded. Finally, numerical examples are provided to verify the theoretical results and to show the convergence behavior.

• 제어로봇시스템학회:학술대회논문집
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• 1991.10a
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• pp.736-740
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• 1991

EEG(Electroencephalogram) background signals can be represented as the sun of a conventional AR(Autoregressive) process and an innovation process, or a prediction error process. We have seen that conventional estimation techniques. such as least square estimates(LSE) or Gaussian maximum likelihood estimates(MLE-G) are optimal when the innovation process satisfies the Gaussian or presumed distribution. But when the data are contaminated by outliers, or artifacts, these assumptions are not met and conventional estimation techniques can badly fall and be strongly biased. It is known that EEG can be easily affected by artifacts. So we suggest a robust estimation technique which considerably performs well against those artifacts.

• Journal of Institute of Control, Robotics and Systems
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• v.20 no.1
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• pp.1-5
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• 2014

In this paper, we propose an optimal fixed-lag FIR (Finite-Impulse-Response) smoother for a class of discrete time-varying state-space signal models. The proposed fixed-lag FIR smoother is linear with respect to inputs and outputs on the recent finite horizon and estimates the delayed state so that the variance of the estimation error is minimized with the unbiased constraint. Since the proposed smoother is derived with system inputs, it can be adapted to feedback control system. Additionally, the proposed smoother can give more general solution than the optimal FIR filter, because it reduced to the optimal FIR filter by setting the fixed-lag size as zero. A numerical example is presented to illustrate the performance of the proposed smoother by comparing with an optimal FIR filter and a conventional fixed-lag Kalman smoother.

• KSII Transactions on Internet and Information Systems (TIIS)
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• v.5 no.4
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• pp.649-664
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• 2011

Cooperative spectrum sensing (CSS) with decision fusion is considered as a key technology for tackling the challenges caused by fading/shadowing effects and noise uncertainty in spectrum sensing in cognitive radio. However, most existing solutions assume an error-free decision transmission, which is obviously not the case in realistic scenarios. This paper extends the general decision-fusion-based CSS scheme by considering the fading/shadowing effects and noise corruption in the common control channels. With this more practical model, the fusion centre first estimates the local decisions using a binary minimum error probability detector, and then combines them to get the final result. Theoretical analysis and simulation of this CSS scheme are performed over typical channels, which suggest some performance deterioration compared with the pure case that assumes an error-free decision transmission. Furthermore, the fusion strategy optimization in the proposed cooperation model is also investigated using the Bayesian criteria. The numerical results show that the total error rate of noisy CSS is higher than that of the pure case, and the optimal values of fusion parameter in the counting rule under both cases decrease as the local detection threshold increases.

• ETRI Journal
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• v.33 no.1
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• pp.27-31
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• 2011

This paper addresses estimating the frequency of a cisoid in the presence of white Gaussian noise, which has numerous applications in communications, radar, sonar, and instrumentation and measurement. Due to the nonlinear nature of the frequency estimation problem, there is threshold effect, that is, large error estimates or outliers will occur at sufficiently low signal-to-noise ratio (SNR) conditions. Utilizing the ideas of averaging to increase SNR and weighted linear prediction, an optimal frequency estimator with smaller threshold SNR is developed. Computer simulations are included to compare its mean square error performance with that of the maximum likelihood (ML) estimator, improved weighted phase averager, generalized weighted linear predictor, and single weighted sample correlator as well as Cramer-Rao lower bound. In particular, with smaller computational requirement, the proposed estimator can achieve the same threshold and estimation performance of the ML method.