• 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.

• Bulletin of the Korean Mathematical Society
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• v.40 no.2
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• pp.289-300
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• 2003

We prove a simplified version of the Nash-Moser implicit function theorem in weighted Banach spaces. We relax the conditions so that the linearized equation has an approximate inverse in different weighted Banach spaces in each recurrence step.

• 제어로봇시스템학회:학술대회논문집
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• 2001.10a
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• pp.41.5-41
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• 2001

A novel method is introduced for determining the weights of a regularization network which approximates one-to-many mapping. A conventional neural network will converges to the average value when outputs are multiple for one input. The capability of proposed network is demonstrated by an example of learning inverse mapping.

• Journal of electromagnetic engineering and science
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• v.3 no.2
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• pp.133-139
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• 2003

The nonuniqueness of a mathematically rigorous solution to 2-dimensional inverse scattering problems is explained in a limiting view of the numerical calculations based on the spectral-domain moment method. It is illustrated that its theoretical uniqueness cannot be assured even by performing additional measurements of the scattered fields not only along multiple lines but also with angular/frequency-diversities. In a real situation, however, computational error and measurement noise are inevitable. Those limitations render it meaningless to controvert the existence of a theoretically rigorous solution. Hence the most practical issue is how to remedy the instability of its practically approximate solution.

• International Journal of Control, Automation, and Systems
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• v.4 no.1
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• pp.17-29
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• 2006

A novel inverse kinematics solution based on the back propagation neural network (NN) for redundant manipulators is developed for online obstacles avoidance. A laser transducer at the end-effctor is used for online planning the trajectory. Since the inverse kinematics in the present problem has infinite number of joint angle vectors, a fuzzy reasoning system is designed to generate an approximate value for that vector. This vector is fed into the NN as a hint input vector rather than as a training vector to guide the output of the NN. Simulations are implemented on both three- and four-link redundant planar manipulators to show the effectiveness of the proposed position control system.

• Journal of the Korean Data and Information Science Society
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• v.28 no.3
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• pp.659-668
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• 2017

The inverse Weibull distribution (IWD) can be readily applied to a wide range of situations including applications in medicines, reliability and ecology. It is generally known that the lifetimes of test items may not be recorded exactly. In this paper, therefore, we consider the maximum likelihood estimation (MLE) and Bayes estimation of the entropy of a IWD under generalized progressive hybrid censoring (GPHC) scheme. It is observed that the MLE of the entropy cannot be obtained in closed form, so we have to solve two non-linear equations simultaneously. Further, the Bayes estimators for the entropy of IWD based on squared error loss function (SELF), precautionary loss function (PLF), and linex loss function (LLF) are derived. Since the Bayes estimators cannot be obtained in closed form, we derive the Bayes estimates by revoking the Tierney and Kadane approximate method. We carried out Monte Carlo simulations to compare the classical and Bayes estimators. In addition, two real data sets based on GPHC scheme have been also analysed for illustrative purposes.

• 제어로봇시스템학회:학술대회논문집
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• 2001.10a
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• pp.93.4-93
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• 2001

Based on input and output data pairs of nonlinear systems, this paper proposes a simple and effective Just-In-Time (JIT) method, called Direct JIT Control, for nonlinear control design. It uses an inverse model of controlled plant to compute an initial control action, and then adapts the initial control action by adding a fine-tuning control action, depended on the errors between the real outputs and the expected reference signals. Meanwhile, the proposed JIT method accomplishes the adaptation of the inverse model just simply by means of the refreshment of input and output data pairs. In addition, the JIT modeling technique guarantees this method to obtain an approximate inverse model of the controlled nonlinear plant in the neighborhood of a query. Based on a ...

• Proceedings of the Korean Society of Precision Engineering Conference
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• 1996.04a
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• pp.661-665
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• 1996

An inverse kinemetics problem of a reclaimer which digs and transports ironstones or coals in the raw yard is investigated. Because of the special features of the reclaimer of which scooping buckets are attached around the rotating drum at the end of boom, kinematic redundancy occurs in determining the joint varialbes For a given reclaiming point in space the forward kinematics yields 3 equations, however the number of involved variables in the equations are four. A plane equation approximating the surface near a reclaiming point is obtained by considering 8 adjacent points surrounding the reclaiming point. One extra equation to overcome redunduncyis further obtained from the condition that the normal vector at a reclaiming point is perpendicular to the plane. An approximate solution for a simplified problem is first discussed, Numerical solution for the oritinal nonlinear porblem with a constraint equation is also investigated. Finally a closed form solution which is not exact but sufficiently close enough is proposed by exploiting geometric constraint.

• Communications for Statistical Applications and Methods
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• v.27 no.4
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• pp.469-486
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• 2020

Entropy is an important term in statistical mechanics that was originally defined in the second law of thermodynamics. In this paper, we consider the maximum likelihood estimation (MLE), maximum product spacings estimation (MPSE) and Bayesian estimation of the entropy of an inverse Weibull distribution (InW) under a generalized type I progressive hybrid censoring scheme (GePH). The MLE and MPSE of the entropy cannot be obtained in closed form; therefore, we propose using the Newton-Raphson algorithm to solve it. Further, the Bayesian estimators for the entropy of InW based on squared error loss function (SqL), precautionary loss function (PrL), general entropy loss function (GeL) and linex loss function (LiL) are derived. In addition, we derive the Lindley's approximate method (LiA) of the Bayesian estimates. Monte Carlo simulations are conducted to compare the results among MLE, MPSE, and Bayesian estimators. A real data set based on the GePH is also analyzed for illustrative purposes.

• Proceedings of the KSME Conference
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• 2001.06b
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• pp.48-52
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• 2001

In this paper presents an accurate AFM used that is free from the Z-directional distortion of a servo actuator is described. Two mathematical correction methods by the in-situ self-calibrationare employed in this AFM. One is the method by the integration, and the other is the method by inverse function of the calibration curve. The in situ self-calibration method by the integration, the derivative of the calibration curve function of the PZT actuator is calculated from the profile measurement data sets which are obtained by repeating measurements after a small Z-directional shift. Input displacement at each sampling point is approximately estimated first by using a straight calibration line. The derivative is integrated with reference to the approximate input to obtain the approximate calibration curve. Then the approximation of the input value of each sampling point is improved using the obtained calibration curve. Next the integral of the derivative is improved using the newly estimated input values. As a result of repeating these improving process, the calibration curve converges to the correct one, and the distortion of the AFM image can be corrected. In the in situ self-calibration through evaluating the inverse function of the calibration curve, the profile measurement data sets were used during the data processing technique. Principles and experimental results of the two methods are presented.