• Journal for History of Mathematics
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• v.24 no.2
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• pp.1-15
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• 2011

Approximation is a very useful approach in mathematics research. It was the same in traditional Chinese and Chosun mathematics. This study derived five characteristics from approximation approaches which were found in Chinese and Chosun mathematical books: improvement of approximate values, common and inevitable use of approximate values, recognition of approximate values and their reasons, comparison of their exactness, application of approximate principles. Through these characteristics, we can infer what Chinese and Chosun mathematicians recognized approximate values and how they manipulated them. They took approximate approaches by necessity or for the sake of convenience in mathematical study and its applications. Also, they tried to improve the degree of exactness of approximate values and use the inverse calculations to check them.

• Journal of the Korean Society of Surveying, Geodesy, Photogrammetry and Cartography
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• v.30 no.6_2
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• pp.593-605
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• 2012

LiDAR systems provide dense and accurate topographic information. A pre-requisite to achieving the potential accuracy of LiDAR is having a proper system calibration, which aims at estimating all the systematic errors in the system measurements and the mounting parameters relating the different components. This paper presents a rigorous and two approximate methods for LiDAR system calibration. The rigorous approach makes use of the LiDAR equation and the system raw measurements. The approximate approaches utilize simplified LiDAR equations using some assumptions, which allow for less strict requirements regarding the raw measurements. The first presented approximate method, denoted as quasi-rigorous, assumes that we are dealing with a vertical platform (i.e., small pitch and roll angles). This method requires time-tagged point cloud and trajectory position data. The second approximate method, denoted as simplified, assumes that we are dealing with parallel strips, vertical platform, and minor terrain elevation variations compared to the flying height above ground. Such method can be performed using the LiDAR point cloud only. Experimental results using a real dataset, whose characteristics deviate to some extent from the utilized assumptions in the approximate methods, are presented to provide a comparative analysis of the outcome from the introduced methods.

• Journal of Korean Society of Industrial and Systems Engineering
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• v.38 no.3
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• pp.8-13
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• 2015

One of the most usual indicators to measure the performance of any inventory policy is the mean physical stock. In general, when estimating the mean physical stock in periodic review inventory systems, approximate approaches are often utilized by practitioners and researchers. The mean physical stock is generally calculated by a simple approximation. Still these simple methods are frequently used to analyze various single stockpoint and multi-echelon inventory systems. However, such a simple approximation can be very inaccurate. This is particularly true for low service levels. Even though exact methods to calculate the mean physical stock have been derived, they are available for specific cases only and computationally not very efficient, and therefore less useful in practice. In literature, approximate approaches, such as the simple, the linear, and Simpson approximations, were derived for the periodic review inventory systems that allow backorders. This paper modifies the approximate approaches for the lost sales case and evaluates the modified approximate approaches. Through computational experiments, average (and maximum) percentage deviations of mean physical stock between the exact method and the modified approximations are compared in the periodic review inventory system with lost sales. The same comparison between the modified and the original approximations are also conducted, in order to examine the performance of modified approximations. The results show that all modified approximations perform well for high service levels, but also that the performance may deteriorate fast with decreasing service level. The modified Simpson approximation is clearly better. In addition, the comparison between the modified and the original approximations in the periodic review inventory system with lost sales shows that the modified approximation outperforms the original approximation.

• Proceedings of the Korean Statistical Society Conference
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• 2003.05a
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• pp.167-170
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• 2003

We develop semiparametric methods for matched case-control studies using regression splines. Three methods are developed: an approximate crossvalidation scheme to estimate the smoothing parameter inherent in regression splines, as well as Monte Carlo Expectation Maximization (MCEM) and Bayesian methods to fit the regression spline model. We compare the approximate cross-validation approach, MCEM and Bayesian approaches using simulation, showing that they appear approximately equally efficient, with the approximate cross-validation method being computationally the most convenient. An example from equine epidemiology that motivated the work is used to demonstrate our approaches.

• Journal of the Korean Operations Research and Management Science Society
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• v.30 no.1
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• pp.161-176
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• 2005

In a situation that ordinal preferences on multiattribute weights are captured, we present two solution approaches: an exact approach and an approximate method. The former, an exact solution approach via interaction with a decision-maker, pursues the progressive reduction of a set of non-dominated alternatives by narrowing down the feasible attribute weights region. Subsequent interactive questions and responses, however, sometimes may not guarantee the best alternative or a complete rank order of a set of alternatives that the decision-maker desires to have. Approximate solution approaches, on the other hand, can be divided into three categories including surrogate weights methods, dominance value-based decision rules, and three classical decision rules. Their efficacies are evaluated in terms of choice accuracy via a simulation analysis. The simulation results indicate that a proposed hybrid approach, intended to combine an exact solution approach through interaction and a dominance value-based approach, is recommendable for aiding a decision making in a case that a final choice is seldom made at single step under attribute weights that are imprecisely specified beyond ordinal descriptions.

• Proceedings of the Korean Institute of Intelligent Systems Conference
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• 1998.06a
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• pp.719-724
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• 1998

This paper presents a systematic developement of a formal approach to inference in approximate reasoning. We introduce some measures of similarity and discuss their properties. Using the concept of similarity index we formulate two methods for inferring from vague knowledge. In order to illustrate the effectiveness of the proposed technique we use it to develop a vowel recognition system.

• Proceedings of the Korean Society of Computational and Applied Mathematics Conference
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• 2003.09a
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• pp.15-15
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• 2003

We provide some recent results of approximation algorithms for solving Markov Games and discuss their applications to problems that arise in Computer Science. We consider a receding horizon approach as an approximate solution to two-person zero-sum Markov games with an infinite horizon discounted cost criterion. We present error bounds from the optimal equilibrium value of the game when both players take “correlated” receding horizon policies that are based on exact or approximate solutions of receding finite horizon subgames. Motivated by the worst-case optimal control of queueing systems by Altman, we then analyze error bounds when the minimizer plays the (approximate) receding horizon control and the maximizer plays the worst case policy. We give two heuristic examples of the approximate receding horizon control. We extend “parallel rollout” and “hindsight optimization” into the Markov game setting within the framework of the approximate receding horizon approach and analyze their performances. From the parallel rollout approach, the minimizing player seeks to combine dynamically multiple heuristic policies in a set to improve the performances of all of the heuristic policies simultaneously under the guess that the maximizing player has chosen a fixed worst-case policy. Given $\varepsilon$>0, we give the value of the receding horizon which guarantees that the parallel rollout policy with the horizon played by the minimizer “dominates” any heuristic policy in the set by $\varepsilon$, From the hindsight optimization approach, the minimizing player makes a decision based on his expected optimal hindsight performance over a finite horizon. We finally discuss practical implementations of the receding horizon approaches via simulation and applications.

• International Journal of Fuzzy Logic and Intelligent Systems
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• v.13 no.1
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• pp.19-30
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• 2013

Recently, the constrained index tracking problem, in which the task of trading a set of stocks is performed so as to closely follow an index value under some constraints, has often been considered as an important application domain for control theory. Because this problem can be conveniently viewed and formulated as an optimal decision-making problem in a highly uncertain and stochastic environment, approaches based on stochastic optimal control methods are particularly pertinent. Since stochastic optimal control problems cannot be solved exactly except in very simple cases, approximations are required in most practical problems to obtain good suboptimal policies. In this paper, we present a procedure for finding a suboptimal solution to the constrained index tracking problem based on approximate dynamic programming. Illustrative simulation results show that this procedure works well when applied to a set of real financial market data.

• Journal of Mechanical Science and Technology
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• v.14 no.9
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• pp.968-977
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• 2000

The motion of an aircraft landing gear over a rough runway can be modeled by a nonclassically damped system subject to nonstationary random excitations. In this paper, the approximate analysis methods based on either the real or complex normal modes for the computation of nonstationary response covariances are proposed. It has been found by simulation involving a realistic example that, for the nonclassically damped random vibrational systems, the approximate solution method based on the complex normal mode is superior to other approaches with respect to the accuracy and computation time.

• 한국전산유체공학회:학술대회논문집
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• 2005.10a
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• pp.99-104
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• 2005

For the efficient reliability analysis, Bi-direction two-point approximation(BTPA) method is developed which solves shortcomings of conventional two-point approximation(TPA) methods that generate an approximate surface with low accuracy or sometimes do an unstable approximate surface. The conventional reliability based design optimization(RBDO) methods require high computational cost compared with the deterministic design optimization(DO) methods. To overcome the computational inefficiency of RBDO, the approximate reliability analysis approaches on the TPA surface are proposed. Using these FORM and SORM analysis strategies, multi-point aerodynamic-structure interacted shape design optimizations with uncertainty are performed very efficiently.