• 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.

• Journal of Convergence for Information Technology
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• v.11 no.11
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• pp.51-56
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• 2021

In this paper, performance degradation in the cross-eye jamming due to amplitude mismatch of two jamming antennas is considered. The mismatch of the amplitude ratio is modeled as a random variable with a normal distribution of the difference between the actual amplitude ratio and the nominal amplitude ratio due to mechanical defects. In the proposed analytic performance analysis, the first-order Taylor series expansion and the second-order Taylor series expansion is adopted. Performance measure of the cross-eye jamming is the mean square difference (MSD). The analytically derived MSD is validated by comparing the analytically derived MSD with the first-order Taylor series-based simulation-based MSD and the second-order Taylor series-based simulation-based MSD. It shows that the analysis-based MSD is superior to the Monte-Carlo-based MSD, which has a high calculation cost.

• Journal of Broadcast Engineering
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• v.23 no.2
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• pp.302-315
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• 2018

Highly non-linear electro-optical transfer function of the Perceptual Quantizer was approximated by a truncated Taylor series, resulting in a closed form solution for luma adjustment. This previous solution is fast and quite suitable for the hardware implementation of luma adjustment, but the approximation error becomes relatively large in the range of 600~3,900 cd/m2 linear light. In order to reduce such approximation error, we propose a new linear model, for which a correction is performed on the position and the slope of line based on the scope of approximation. In order to verify the approximation capability of the proposed linear model, a comparative study on the luma adjustment schemes was conducted using various high dynamic range test video sequences. Via the comparative study, we identified a significant performance enhancement over the previous fast luma adjustment scheme, where a 4.65dB of adjusted luma t-PSNR gain was obtained for a test sequence having a large portion of saturated color pixels.

• KSCE Journal of Civil and Environmental Engineering Research
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• v.13 no.1
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• pp.39-46
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• 1993

The need to develop method which can improve the shape design efficiency using high quality approximation is being brought up. In this study, to perform shape optimal design of three-dimensional continuum structures an efficient approximation method for stress constraints is proposed, based on expanding the nodal forces in Taylor series with respect to shape variables. Numerical examples are performed using the 3-D cantilever beam and fixed-fixed beam and compared with other method to demonstrate the efficiency and convergence rate of the Force Approximation method. It is shown that by taking advantage of this high quality approximation, the total number of finite element analysis required for shape optimization of 3-D continuum structures can be reduced significantly, resulting to the same level of efficiency achieved previously in sizing optimization problems. Also, shape representation by super curve technique applied to obtain optimal shape finds useful method.

• Journal of Institute of Control, Robotics and Systems
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• v.18 no.3
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• pp.175-180
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• 2012

A nonlinear navigation filter for biomimetic robot using analytic approximation of mean and covariance of state variable is proposed. The approximations are performed at the time update step in the filter structure. The mean is approximated to the 3rd order of Taylor's series expansion of true mean and the covariance is approximated to the 3rd order either. The famous EKF is a nonlinear filtering method approximating the mean to 1st order and the covariance to the 3rd order. The UKF approximate them to the higher orders by numerical method. The proposed method derived a analytical approximation of them for navigation system and therefore don't need so called sigma point transformation in UKF. The simulation results show that the proposed method can be a good alternative of UKF in the systems which require less computational burden.

• Proceedings of the KIEE Conference
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• 2003.11c
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• pp.946-949
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• 2003

In this paper, a DDFS(Direct Digital Frequency Synthesis)chip has been designed focusing on the reduction of ROM size and implemented using FPGA. When calculating the sine value for the input phase value, we used the Taylor series expansion approximation method to reduce the number of addresses of ROM. We also used the piecewise straight line approximation method, ie, the stored value int the ROM is the difference of the sine value and the straight line approximation. Using this method, we could reduce four bits for each ROM data.

• Journal of the Korean Data and Information Science Society
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• v.25 no.3
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• pp.643-653
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• 2014

In this paper, we propose some estimators for the extreme value distribution based on the interval method and mid-point approximation method from the progressive Type-I interval censored sample. Because log-likelihood function is a non-linear function, we use a Taylor series expansion to derive approximate likelihood equations. We compare the proposed estimators in terms of the mean squared error by using the Monte Carlo simulation.

• KSCE Journal of Civil and Environmental Engineering Research
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• v.10 no.3
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• pp.7-17
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• 1990

The objective of this paper is to provide a method of optimizing are as of the members as well as shape of both truss and arch structures. The design process includes satisfaction of stress and Euler buckling stress constraints for truss and combined stress constraints for arch structures. In order to reduce the number of detailed finite element analysis, the Force Approximation Method is used. A finite element analysis of the initial structure is performed and the gradients of the member end forces are calculated with respect to the areas and nodal coordinates. The gradients are used to form an approximate structural analysis based on first order Taylor series expansions of the member end forces. Using move limits, a numerical optimizer minimizes the volume of the structure with information from the approximate structural analysis. Numerical examples are performed and compared with other methods to demonstrate the efficiency and reliability of the Force Approximation Method for shape optimization. It is shown that the number of finite element analysis is greatly reduced and that it leads to a highly efficient method of shape optimization of structures.

• Communications for Statistical Applications and Methods
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• v.15 no.2
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• pp.147-159
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• 2008

We consider using ranked set sampling methods to draw inference about the three well-known measures of overlap, namely Matusita's measure $\rho$, Morisita's measure $\lambda$ and Weitzman's measure $\Delta$. Two exponential populations with different means are considered. Due to the difficulties of calculating the precision or the bias of the resulting estimators of overlap measures, because there are no closed-form exact formulas for their variances and their exact sampling distributions, Monte Carlo evaluations are used. Confidence intervals for those measures are also constructed via the bootstrap method and Taylor series approximation.

• The Journal of Korean Institute of Communications and Information Sciences
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• v.21 no.11
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• pp.2942-2953
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• 1996

This paper studies the effect of intersymbol interference due to sampling-time jitter on the worst-case bit error probability in a digital modultation over an additive white Gaussian noise channel, with the squared-root raised-cosine filters in the transmitter and the receiver. It derives approximation formulas using the Taylor series approximations. the principal results of this paper is the relationship between the worst-casse bit error probability, the degree of jitter, the roll factor of the raised cosine filter, and other quantities. Numerical results show, as expected, that the intersymbol interference decreases as the roll-off factor increases and the jitter decreases. They also show that the approximation formulas are accurate for smally intersymbol interference, i.e., for large roll-noise ratio $E_{b/}$ $N_{0}$.leq.7 dB and begin to lose accuracy for larger signal-to-noise ratio.o.o.