• Journal of the Institute of Electronics Engineers of Korea SD
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• v.46 no.3
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• pp.20-25
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• 2009

We propose hardware architecture of floating-point square root and inverse square root arithmetic units using lookup tables. They are used for lighting engines and shader processor for 3D graphic processing. The architecture is based on Taylor series expansion and consists of lookup tables and correction units so that the size of look-up tables are reduced. It can be applied to 32 bit floating point formats of IEEE-754 and reduced 24 bit floating point formats. The square root and inverse square root arithmetic units for 32 bit and 24 bit floating format number are designed as the proposed architecture. They can operation in a single cycle, and satisfy the precision of $10^{-5}$ required by OpenGL 1.x ES. They are designed using Verilog-HDL and the RTL codes are verified using an FPGA.

• Journal of the Korea Institute of Information and Communication Engineering
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• v.11 no.1
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• pp.46-55
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• 2007

The Newton-Raphson's algorithm for finding a floating point reciprocal and inverse square root calculates the result by performing a fixed number of multiplications. In this paper, an improved Newton-Raphson's algorithm is proposed, that performs multiplications a variable number. Since the number of multiplications performed by the proposed algorithm is dependent on the input values, the average number of multiplications per an operation is derived from many reciprocal and inverse square tables with varying sizes. The superiority of this algorithm is proved by comparing this average number with the fixed number of multiplications of the conventional algorithm. Since the proposed algorithm only performs the multiplications until the error gets smaller than a given value, it can be used to improve the performance of a reciprocal and inverse square root unit. Also, it can be used to construct optimized approximate tables. The results of this paper can be applied to many areas that utilize floating point numbers, such as digital signal processing, computer graphics, multimedia, scientific computing, etc.

• Journal of Korea Multimedia Society
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• v.22 no.9
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• pp.1029-1035
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• 2019

In this paper, a tentative Kth order Goldschmidt floating point number Nth root algorithm for K order convergence rate in one iteration is proposed by applying Taylor series to the Goldschmidt square root algorithm. Using the proposed algorithm, Nth root and Nth inverse root can be computed from iterative multiplications without division. It also predicts the error of the algorithm iteration. It iterates until the predicted error becomes smaller than the specified value. Since the proposed algorithm only performs the multiplications until the error gets smaller than a given value, it can be used to improve the performance of a floating point number Nth root unit.

• Journal of the Korea Institute of Information and Communication Engineering
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• v.13 no.8
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• pp.1593-1600
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• 2009

There are two major algorithms to find a square root of floating point number, one is the Newton_Raphson algorithm and GoldSchmidt algorithm which calculate it approximately by iterating multiplications and the other is SRT algorithm which calculates it exactly by iterating subtractions. This paper proposes an exact floating point square root algorithm using only multiplication. At first an approximate inverse square root is calculated by Newton_Raphson algorithm, and then an exact square root algorithm by reducing an error in it and a compensation algorithm of it are proposed. The proposed algorithm is verified to calculate all of numbers in a single precision floating point number and 1 billion random numbers in a double precision floating point number. The proposed algorithm requires only the multipliers without another hardware, so it can be widely used in an embedded system and mobile production which requires an efact square root of floating point number.

• Korea Science and Art Forum
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• v.30
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• pp.41-56
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• 2017

This study is an intensive study on Tae Rin Lee's research results. A linear system for Estimating the Strength of Super Personal Conflict (ESSPC) in animations is proposed. Tae Rin Lee has extracted the Super Personal Conflict (SPC) shots of animations, and obtained the strength through the experts' psychological test experiment. The purpose of this study is to find a model that automatically computes the superpersonal conflict intensity value (ESSPC). By utilizing these results, 1) 20 image feature vectors are suggested for analyzing the SPC, and 2) a linear system is found for auto-calculating ESSPC by using the pseudo inverse matrix. The proposed system shows 9.25% root mean square error and the effectiveness is proven.

• Journal of the Korean Association of Geographic Information Studies
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• v.13 no.3
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• pp.29-41
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• 2010

In this study, the prediction errors of various spatial interpolation methods used to model values at unmeasured locations was compared and the accuracy of these predictions was evaluated. The root mean square (RMS) was calculated by processing different parameters associated with spatial interpolation by using techniques such as inverse distance weighting, kriging, local polynomial interpolation and radial basis function to known elevation data of the east coastal area under the same condition. As a result, a circular model of simple kriging reached the smallest RMS value. Prediction map using the multiquadric method of a radial basis function was coincident with the spatial distribution obtained by constructing a triangulated irregular network of the study area through the raster mathematics. In addition, better interpolation results can be obtained by setting the optimal power value provided under the selected condition.

• Communications for Statistical Applications and Methods
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• v.27 no.1
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• pp.97-108
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• 2020

This paper compares several methods for estimating parameters of normal inverse Gaussian distribution. Ordinary maximum likelihood estimation and the method of moment estimation often do not work properly due to restrictions on parameters. We examine the performance of adjusted estimation methods along with the ordinary maximum likelihood estimation and the method of moment estimation by simulation and real data application. We also see the effect of the initial value in estimation methods. The simulation results show that the ordinary maximum likelihood estimator is significantly affected by the initial value; in addition, the adjusted estimators have smaller root mean square error than ordinary estimators as well as less impact on the initial value. With real datasets, we obtain similar results to what we see in simulation studies. Based on the results of simulation and real data application, we suggest using adjusted maximum likelihood estimates with adjusted method of moment estimates as initial values to estimate the parameters of normal inverse Gaussian distribution.

• Korean Journal of Air-Conditioning and Refrigeration Engineering
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• v.20 no.3
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• pp.205-212
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• 2008

This paper describes the application of an inverse building model to a calibrated forward building model using EnergyPlus program. Typically, inverse models are trained using measured data. However, in this study, an inverse building model was trained using data generated by an EnergyPlus model for an actual office building. The EnergyPlus model was calibrated using field data for the building. A training data set for a month of July was generated from the EnergyPlus model to train the inverse model. Cooling load prediction of the trained inverse model was tested using another data set from the EnergyPlus model for a month of August. Predicted cooling loads showed good agreement with cooling loads from the EnergyPlus model with root-mean square errors of 4.11%. In addition, different control strategies with dynamic cooling setpoint variation were simulated using the inverse model. Peak cooling loads and daily cooling loads were compared for the dynamic simulation.

• Korean Journal of Air-Conditioning and Refrigeration Engineering
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• v.22 no.7
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• pp.468-473
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• 2010

This paper deals with approximate integral solutions to the one-dimensional model describing the charging process of stratified thermal storage tanks. Temperature is assumed to be the form of Fermi-Dirac distribution function, which can be separated to two sets of cubic polynomials for each hot and cold side of thermal boundary layers. Proposed approximate integral solutions are compared to the previous works of the approximate analytic solutions and show reasonable agreement. The approach, however, has benefits in mathematical difficulties, complicated solution form and unstable convergence of series solution founded in the previous analytic solutions. Solutions for a semi-infinite region, which have simple closed form solutions, give close agreement to those for a finite region. Thermocline thickness is obtained in closed form and shows proportional behavior to the square root of time and inverse proportional behavior to the square root of flow rate.

• Journal of the Korean Data and Information Science Society
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• v.27 no.6
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• pp.1465-1475
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• 2016

In order to secure safe meals, the hazards of microorganisms associated with food poisoning accident should be monitored and controlled in real situations. It is necessary to determined the correlation between existing common bacteria number (aerobic plate count; APC) and RLU (relative light unit) in cookware. In this paper, we investigate the correlation between ATP (RUL) and APC (CFU) by using three types of transform (inverse, square root, log transforms) of raw data in two steps. Among these transforms, the log transform at the first step has been found to be optimal for the data of cutting board, knife, soup bowl (stainless), and tray (carbon). The square root-inverse and the square root-square root transform at the second step have been shown to be optimal respectively for the cup and for the soup bowl (carbon) data.