• Nuclear Engineering and Technology
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• v.31 no.2
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• pp.172-181
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• 1999

Series expansion methods to compute the exponential of a matrix have been compared by applying them to fuel depletion calculations. Specifically, Taylor, Pade, Chebyshev, and rational Chebyshev approximations have been investigated by approximating the exponentials of bum matrices by truncated series of each method with the scaling and squaring algorithm. The accuracy and efficiency of these methods have been tested by performing various numerical tests using one thermal reactor and two fast reactor depletion problems. The results indicate that all the four series methods are accurate enough to be used for fuel depletion calculations although the rational Chebyshev approximation is relatively less accurate. They also show that the rational approximations are more efficient than the polynomial approximations. Considering the computational accuracy and efficiency, the Pade approximation appears to be better than the other methods. Its accuracy is better than the rational Chebyshev approximation, while being comparable to the polynomial approximations. On the other hand, its efficiency is better than the polynomial approximations and is similar to the rational Chebyshev approximation. In particular, for fast reactor depletion calculations, it is faster than the polynomial approximations by a factor of ∼ 1.7.

• Transactions of the Korean Society of Mechanical Engineers
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• v.19 no.2
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• pp.433-442
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• 1995

For the line search of a multi-variable optimization, an efficient algorithm is presented. The algorithm sequentially employs several polynomial approximations such as 2-point quadratic interpolation, 3-point cubic interpolation/extrapolation and 4-point cubic interpolation/extrapolation. The order of polynomial function is automatically increased for improving the accuracy of approximation. The method of approximation (interpolation or extrapolation) is automatically switched by checking the slope information of the sample points. Also, for selecting the initial step length along the descent vector, a new approach is presented. The performance of the proposed method is examined by solving typical test problems such as mathematical problems, mechanical design problems and dynamic response problems.

• Journal of applied mathematics & informatics
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• v.27 no.1_2
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• pp.139-147
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• 2009

We study the neural network approximation to a function in $C^1$[0, 1] and its derivative. In [3], we used even trigonometric polynomials in order to get an approximation order to a function in $L_p$ space. In this paper, we show the simultaneous approximation order to a function in $C^1$[0, 1] using a Bernstein polynomial and a feedforward neural network. Our proofs are constructive.

• Journal of Korean Institute of Industrial Engineers
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• v.27 no.4
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• pp.379-383
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• 2001

The restricted shortest path problem is known to be weakly NP-hard and solvable in pseudo-polynomial time. Four fully polynomial approximation schemes (FPAS) are available in the literature, and most of these are based on pseudo-polynomial algorithms. In this paper, we propose a new FPAS that can be easily derived from a combination of a set of standard techniques. Although the complexity of the suggested algorithm is not as good as the fastest one available in the literature, it is practical in the sense that it does not rely on the bound tightening phase based on approximate binary search as in Hassin's fastest algorithm. In addition, we provide a review of standard techniques of existing works as a useful reference.

• Kyungpook Mathematical Journal
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• v.49 no.1
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• pp.57-65
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• 2009

In the papers [5]-[7] was examined approximation of functions by the modified Sz$\'{a}$sz-Mrakyan operators and other positive linear operators preserving $e_2(x)=x^2$. In this paper we introduce the Post-Widder and Stancu operators preserving $x^2$ in polynomial weighted spaces. We show that these operators have better approximation properties than classical Post-Widder and Stancu operators.

• Journal of KIISE:Computer Systems and Theory
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• v.30 no.7_8
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• pp.387-396
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• 2003

This paper provides an approximation algorithm for STP-MSP(Steiner Tree Problem with minimum number of Steiner Points).Because it seems to be impossible to have a PTAS(Polynomial Time Approximation Schemes), which gives the near optimal solutions, for the problem, the algorithm of this paper is an alternative that has the approximation ratio 2 with $n^{O(1)}$ run time. The importance of this paper is the potential to solve other related unsolved problems. The idea of this paper is to distribute the error allowance over the problem instance so that we may reduce the run time to polynomial bound out of infinitely many cases. There are earlier works[1,2] that show the approximations that have practical run times with the ratio of bigger than 2, but this paper shows the existence of a poly time approximation algorithm with the ratio 2.

• Journal of the Korean Society for Industrial and Applied Mathematics
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• v.13 no.4
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• pp.307-314
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• 2009

In this work, we introduce a new quatnary approximating subdivision scheme for curve and deal with its analysis (convergence and regularity) using Laurent polynomials method. We also discuss various properties, such as approximation order and support of basic limit function.

• Communications for Statistical Applications and Methods
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• v.2 no.2
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• pp.376-386
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• 1995

Designs for polynomial approximation to the unknown response function are considered. Optimality criteria are monotone functions of the mean squared error matrix of the least squares estimator. They correspond to the classical A-, D-, G- and Q-optimalities. Optimal first order designs are chosen from the invariant designs and then compared with optimal second order designs.

• Journal of the Korean Society for Industrial and Applied Mathematics
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• v.9 no.2
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• pp.99-106
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• 2005

We present a relation between the orthogonality of the constrained Legendre polynomials over the triangular domain and the BB ($B{\acute{e}zier}\;-Bernstein$) coefficients of the polynomials using the equivalence of orthogonal complements. Using it we also show that the best constrained degree reduction of polynomials in BB form equals the best approximation of weighted Euclidean norm of coefficients of given polynomial in BB form from the coefficients of polynomials of lower degree in BB form.

• Journal of Biomedical Engineering Research
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• v.28 no.5
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• pp.665-675
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• 2007

The morphological change of ECG is the important diagnostic parameter to finding the malfunction of a heart. Generally ST segment deviation is concerned with myocardial abnormality. The aim of this study is to detect the change of ST in shape using a polynomial approximation method and the reference ST type. The developed algorithm consists of feature point detection, ST level detection and ST shape classification. The detection of QRS complex is accomplished using it's the morphological characteristics such as the steep slope and high amplitude. The developed algorithm detects the ST level change, and then classifies the ST shape type using the polynomial approximation. The algorithm finds the least squares curve for the data between S wave and T wave in ECG. This curve is used for the classification of the ST shapes. ST type is classified by comparing the slopes of the specified points between the reference ST set and the least square curve. Through the result from the developed algorithm, we can know when the ST level change occurs and what the ST shape type is.