• Bulletin of the Korean Mathematical Society
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• v.36 no.4
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• pp.629-636
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• 1999

We introduce Lipschitz algebras of differentiable functions of a perfect compact plane set X and extend the definition to Lipschitz algebras of infinitely differentiable functions of X. Then we define the subalgebras generated by polynomials, rational functions, and analytic functions in some neighbourhood of X, and determine the maximal ideal spaces of some of these algebras. We investigate the polynomial and rational approximation problems on certain compact sets X.

• Journal of the Korean Society for Industrial and Applied Mathematics
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• v.3 no.1
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• pp.81-98
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• 1999

In spite of the well developed theory and the practical use of the univariate B-spline, the theory of multivariate B-spline is very new and waits its practical use. We compare in this article the multivariate B-spline approximation with the polynomial approximation for the surface fitting. The graphical and numerical comparisons show that the multivariate B-spline approximation gives much better fitting than the polynomial one, especially for the surfaces which vary very rapidly.

• Journal of KIISE:Computer Systems and Theory
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• v.31 no.10
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• pp.562-574
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• 2004

We address the problem of energy-optimal voltage scheduling for fixed-priority hard real-time systems. First, we prove that the problem is NP-hard. Then, we present a fully polynomial time approximation scheme (FPTAS) for the problem. for any $\varepsilon$>0, the proposed approximation scheme computes a voltage schedule whose energy consumption is at most (1+$\varepsilon$) times that of the optimal voltage schedule. Furthermore, the running time of the proposed approximation scheme is bounded by a polynomial function of the number of input jobs and 1/$\varepsilon$. Experimental results show that the approximation scheme finds more efficient voltage schedules faster than the best existing heuristic.

• Journal of the Korean Operations Research and Management Science Society
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• v.28 no.4
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• pp.191-198
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• 2003

The generalized knapsack problem or gknap is the combinatorial optimization problem of optimizing a nonnegative linear function over the integral hull of the intersection of a polynomially separable 0-1 polytope and a knapsack constraint. The knapsack, the restricted shortest path, and the constrained spanning tree problem are a partial list of gknap. More interesting1y, all the problem that are known to have a fully polynomial approximation scheme, or FPTAS are gknap. We establish some necessary and sufficient conditions for a gknap to admit an FPTAS. To do so, we recapture the standard scaling and approximate binary search techniques in the framework of gknap. This also enables us to find a weaker sufficient condition than the strong NP-hardness that a gknap does not have an FPTAS. Finally, we apply the conditions to explore the fully polynomial approximability of the constrained spanning problem whose fully polynomial approximability is still open.

• The Transactions of the Korean Institute of Electrical Engineers
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• v.36 no.9
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• pp.660-669
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• 1987

Routh approximation method is the most computationally attractive. But this method may cause time-response error because this method does not match the time-response directly. In this paper a new mixed method for obtaining stable reduced-order models for high-order continuous-time systems is proposed. It makes use of the advantages of the Routh approximation method and the Minimization of Integral Squared Error(MISE) criterion approach. In this mixed method the characteristic polynomial of the reduced-order model is first obtained from that of original system by using the Auxiliary Denominator Polynomial(ADP). The numerator polynomial is then determined so as to minimize the intergral squared-error of unit step responses. The advantages of the propsed method are that the reduced models are always stable if the original system are stable and the frequency domain and time domain characteristic of the original system will be preserved in the reduced models.

• Journal of Institute of Control, Robotics and Systems
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• v.8 no.8
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• pp.691-697
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• 2002

Myocardial ischemia is a disorder of cardiac function caused by insuficient blood flow to the muscle tissue of the heart. We can diagnose myocardial ischemia by observing the change of ST-segment, but this change is temporary. Our primary purpose is to detect the temporary change of the 57-segment automatically In the signal processing, the wavelet transform decomposes the ECG(electrocardiogram) signal into high and low frequency components using wavelet function. Recomposing the high frequency bands including QRS complex, we can detect QRS complex more easily. Amplitude comparison method is adopted to detect QRS complex. Reducing the effect of noise to the minimum, we grouped ECG by 5 data and compared the amplitude of maximum value. To recognize the ECG .signal pattern, we adopted the polynomial approximation partially and statistical method. The polynomial approximation makes possible to compare some ECG signal with different frequency and sampling period. The ECG signal is divided into small parts based on QRS complex, and then, each part is approximated to the polynomials. After removing the distorted ECG by calculating the difference between the orignal ECG and the approximated ECG for polynomial, we compared the approximated ECG pattern with the database, and we detected and classified abnormality of ECG.

• Journal of the Institute of Electronics Engineers of Korea CI
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• v.48 no.5
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• pp.64-73
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• 2011

The problem of Euclidean minimum spanning tree (EMST) is to connect given nodes in a plane with minimum cost. There are many algorithms for the polynomial time problem as EMST. However, for numerous nodes, the algorithms consume an enormous amount of time to find an optimal solution. In this paper, an approximation scheme using a polynomial time approximation scheme (PTAS) algorithm with dividing and parallel processing for the problem is suggested. This scheme enables to construct a large, approximate EMST within a short duration. Although initially devised for the non-polynomial problem, we employ naive PTAS to construct a vast EMST with dynamic programming. In an experiment, the approximate EMST constructed by the proposed scheme with 15,000 input terminal nodes and 16 partition cells shows 89% and 99% saving in execution time for the serial processing and parallel processing methods, respectively. Therefore, our scheme can be applied to obtain an approximate EMST quickly for numerous input terminal nodes.

• Communications for Statistical Applications and Methods
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• v.16 no.2
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• pp.389-396
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• 2009

Approximations for the null distribution of a test statistic arising in multivariate analysis to test homogeneity of variances and a mixture of two beta distributions by making use of a product of beta baseline density function and a polynomial adjustment, so called beta-polynomial density approximant, are discussed. Explicit representations of density and distribution approximants of interest in each case can easily be obtained. Beta-polynomial density approximants produce good approximation over the entire range of the test statistic and also accommodate even the bimodal distribution using an artificial example of a mixture of two beta distributions.

• Journal of the Korean Institute of Telematics and Electronics
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• v.24 no.4
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• pp.583-589
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• 1987

A new approximation method is proposed for the linear model reduction of high order dynamic systems. This mehtod is based upon the denominator table(D-table) and time moment-matching technique. The denominator table(D-table) is used to obtain the denominator polynomial of reduced-order model, and the numerator polynomial is obtained by time moment-matching method. This proposed method does not require the calculation of the alpha-beta expansion and reciprocal transformation which should be calculadted by Routh approximation method. The advantages of the proposed method are that it is computationally every attractive better than Routh approximation method and the reduced model is stable Il the original system is stable.

• Journal of applied mathematics & informatics
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• v.8 no.1
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• pp.27-44
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• 2001

A fast Poisson solver on irregular domains, based on bound-ary methods, is presented. The harmonic polynomial approximation of the solution of the associated homogeneous problem provides a good practical boundary method which allows a trivial parallel processing for solution evaluation or straightfoward computations of the interface values for domain decomposition/embedding. AMS Mathematics Subject Classification : 65N35, 65N55, 65Y05.