• Journal of the Chungcheong Mathematical Society
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• v.12 no.1
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• pp.157-162
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• 1999

In this paper, we introduce approximate Perron-Stieltjes integral and approximate Roussel derivative and investigate the differentiability of indefinite approximate Perron-Stieltjes integral.

• Journal of the Korean Mathematical Society
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• v.38 no.6
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• pp.1157-1166
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• 2001

This paper answers some old questions about approximate similarity and raises new ones. We provide positive evidence and a technique for finding negative evidence on the question of whether approximate similarity is the equivalence relation generated by approximate equivalence and similarity.

• Transactions of the Korean Society of Mechanical Engineers A
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• v.29 no.6 s.237
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• pp.842-851
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• 2005

In this paper, a new method for constrained optimization of noisy functions is proposed. In approximate optimization using response surface methods, if constraints have severe noise, the approximate feasible region defined by approximate constraints is apt to include some of the infeasible region defined by actual constraints. This can cause the approximate optimum to converge into the infeasible region. In the proposed method, the approximate optimization is performed with the approximate constraints shifted by their deviations, which are calculated using a diagonal quadratic response surface method. This can prevent the approximate optimum from converging into the infeasible region. To fit the objective and constraints into diagonal quadratic models, we select the center and 4 additional points along each axis of design variables as experimental points. The deviation of each function is calculated using the differences between the real and approximate function values at the experimental points. A sequential approximate optimization technique based on the trust region algorithm is adopted to manage approximate models. The proposed approach is validated by solving some design problems. The results of the problems show the effectiveness of the proposed method.

• Journal of the Korean Mathematical Society
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• v.54 no.4
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• pp.1063-1079
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• 2017

Two standard Bessel sequences in a Hilbert $C^*$-module are approximately duals if the distance (with respect to the norm) between the identity operator on the Hilbert $C^*$-module and the operator constructed by the composition of the synthesis and analysis operators of these Bessel sequences is strictly less than one. In this paper, we introduce (a, m)-approximate duality using the distance between the identity operator and the operator defined by multiplying the Bessel multiplier with symbol m by an element a in the center of the $C^*$-algebra. We show that approximate duals are special cases of (a, m)-approximate duals and we generalize some of the important results obtained for approximate duals to (a, m)-approximate duals. Especially we study perturbations of (a, m)-approximate duals and (a, m)-approximate duals of modular Riesz bases.

• IEMEK Journal of Embedded Systems and Applications
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• v.16 no.5
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• pp.233-240
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• 2021

We propose a novel, highly accurate approximate multiplier using different types of inexact 4-2 compressors. The importance of low hardware costs leads us to develop approximate multiplication for error-resilient applications. Several rules are developed when selecting a topology for designing the proposed multiplier. Our highly accurate multiplier design considers the different error characteristics of adopted compressors, which achieves a good error distribution, including a low relative error of 0.02% in the 8-bit multiplication. Our analysis shows that the proposed multiplier significantly reduces power consumption and area by 45% and 26%, compared with the exact multiplier. Notably, a trade-off relationship between error characteristics and hardware costs can be achieved when considering those of existing highly accurate approximate multipliers. In the image blending, edge detection and image sharpening applications, the proposed 8-bit approximate multiplier shows better performance in terms of image quality metrics compared with other highly accurate approximate multipliers.

• Communications for Statistical Applications and Methods
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• v.5 no.3
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• pp.927-934
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• 1998

An approximate parameter orthogonality is defined, which is called an $\alpha$-approximate orthogonality The useful consequences of parameter orthogonality mentioned by Cox and Reid(1987) can be shared by an $\alpha$-approximate orthogonality. If $\alpha\geq1/2$, the consequences of orthogonality and $\alpha$-approximate orthogonality are asymptotically equivalent.

• The Journal of the Korea institute of electronic communication sciences
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• v.17 no.1
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• pp.173-180
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• 2022

Approximate Computing is a promising method for designing hardware-efficient computing systems. Approximate multiplication is one of key operations used in approximate computing methods for high performance and low power computing. An approximate 4-2 compressor can implement hardware-efficient circuits for approximate multiplication. In this paper, we propose an approximate multiplier with low area and low power characteristics. The proposed approximate multiplier architecture is segmented into three portions; an exact region, an approximate region, and a constant correction region. Partial product reduction in the approximation region are simplified using a new 4:2 approximate compressor, and the error due to approximation is compensated using a simple error correction scheme. Constant correction region uses a constant calculated with probabilistic analysis for reducing error. Experimental results of 8×8 multiplier show that the proposed design requires less area, and consumes less power than conventional 4-2 compressor-based approximate multiplier.

• Transactions of the Korean Society of Mechanical Engineers A
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• v.29 no.9 s.240
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• pp.1199-1208
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• 2005

Nowadays, it is performed actively to optimize by using an approximate model. This is called the approximate optimization. In addition, the sequential approximate optimization (SAO) is the repetitive method to find an optimum by considering the convergence of an approximate optimum. In some recent studies, it is proposed to increase the fidelity of approximate models by applying the sequential sampling. However, because the accuracy and efficiency of an approximate model is directly connected with the design area and the termination criteria are not clear, sequential sampling method has the disadvantages that could support an unreasonable approximate optimum. In this study, the SAO is executed by using trust region, Kriging model and Optimal Latin Hypercube design (OLHD). Trust region is used to guarantee the convergence and Kriging model and OLHD are suitable for computer experiment. finally, this SAO method is applied to various optimization problems of highly nonlinear mathematical functions. As a result, each approximate optimum is acquired and the accuracy and efficiency of this method is verified by comparing with the result by established method.

• Bulletin of the Korean Mathematical Society
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• v.33 no.3
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• pp.329-334
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• 1996

The notion of approximate derivative was introduced by Denjoy in 1916 [3]. Khintchine [5] proved that Rolle's theorem holds for approximate derivatives and Tolstoff [8] proved that every approximate derivative is of Baire class 1 and has Darboux property. Goffman and Neugebauer [4] proved the above results of Tolstoff [8] in a different and simplified method. Also they [4] proved indirectly (via Darboux property) that approximate derivatives possess mean value property.

• The Bulletin of The Korean Astronomical Society
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• v.41 no.1
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• pp.49.3-50
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• 2016

Two major radiative transfer (RT) techniques have been developted to model late-type galaxies: approximate RT and Monte Carlo (MC) RT. In the approximate RT, first proposed by Kylafis & Bahcall, only two terms of unscattered (direct) and single-scattered intensities are computed and higher-order multiple scattering components are approximated, saving computing time and cost compared to MC RT. However, the approximate RT can yield errors in regions where multiple scattering effect is significant. In order to examine how significant the errors of the approximate RT are, we compare results of the approximate RT with those of SKIRT, a state-of-the-art MC RT code, which is basically free from the approximation errors by fully incorporating all the multiple scattered intensities. In this study, we present quantitative errors in the approximate RT for late type galaxy models with various optical depths and inclination angles. We report that the approximate RT is not reliable if the central face-on optical depth is intermediate or high (${\tau}_V$ > 3).