• The Journal of Korean Institute of Communications and Information Sciences
• /
• v.38A no.9
• /
• pp.759-764
• /
• 2013

We present a square root algorithm in $F_q$ which generalizes Atkin's square root algorithm [9] for finite field $F_q$ of q elements where $q{\equiv}5$ (mod 8) and Kong et al.'s algorithm [11] for the case $q{\equiv}9$ (mod 16). Our algorithm precomputes ${\xi}$ a primitive $2^s$-th root of unity where s is the largest positive integer satisfying $2^s|q-1$, and is applicable for the cases when s is small. The proposed algorithm requires one exponentiation for square root computation and is favorably compared with the algorithms of Atkin, M$\ddot{u}$ller and Kong et al.

• Proceedings of the Korean Institute of Information and Commucation Sciences Conference
• /
• v.9 no.2
• /
• pp.895-898
• /
• 2005

This paper describes a design of LNS-based divider and square-root circuits which are key arithmetic units in graphic processor and digital signal processor. To achive area-efficient and low-power that is an essential consideration for mobile environment, a fixed-point format of 16.16 is adopted instead of conventional floating-point format. The designed divider and square-root units consist of binary-to-logarithm converter, subtractor, logarithm-to-binary converter. The binary to logarithm converter is designed using combinational logic based on six regions approximation method. As a result, gate count reduction is obtained when compared with conventional lookup approack. The designed units is 3,130 gate count and 1,280 gate count. To minimize average percent error 3.8% and 4.2%. error compensation method is employed.

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

• Proceedings of the IEEK Conference
• /
• 1999.11a
• /
• pp.380-383
• /
• 1999

본 논문은 Booth 알고리즘을 사용하는 새로운 VQB제산기를 제안한다. 본 논문은 Macsorley의 제산 알고리즘에 기본 원리가 같은 제곱근 알고리즘을 추가하였으며, 이를 VQB 알고리즘이라고 명명하였다. 본 논문은 VQB 제산기의 두 가지 설계를 구현하였다. 하나는 계수를 사용하지 않는 설계 (A) 이며, 둘은 [1/2, 2]의 계수군을 사용하는 설계 (B)이다. 설계 (A)는 순환할때마다 2.54 비트의 부분 몫을 결정하며 설계 (B)는 2.74 비트를 결정한다. 본 논문은 VQB 제산기의 성능지표를 좌우하는 제곱근을 위주로 하여 SRT 제산기와의 비교를 시도하였다. VQB 는 처리량과 설계 노력 면에서 SRT를 앞서며, 면적과 임계지연 면에서는 SRT와 서로 견줄만한 수준이다. 표준셀 0.35㎛ CMOS 공정으로 구현될 때, 설계 (A)의 임계지연은 9.69㎱ 이며, 설계 (B)는 11.05㎱이다.

• KSCE Journal of Civil and Environmental Engineering Research
• /
• v.28 no.6A
• /
• pp.835-842
• /
• 2008

The response surface method (RSM) is widely adopted for the structural reliability analysis because of its numerical efficiency. However, the RSM is still time consuming for large-scale applications and sometimes shows large errors in the calculation of sensitivity of reliability index with respect to random variables. Therefore, this study proposes a new RSM in which moving least squares (MLS) approximation is applied. Least squares approximation generally used in the common RSM gives equal weight to the coefficients of the response surface function (RSF). On the other hand, The MLS approximation gives higher weight to the experimental points closer to the design point, which yields the RSF more similar to the limit state at the design point. In the procedure of the proposed method, a linear RSF is constructed initially and then a quadratic RSF is formed using the axial experimental points selected from the reduced region where the design point is likely to exist. The RSF is updated successively by adding one more experimental point to the previously sampled experimental points. In order to demonstrate the effectiveness of the proposed method, mathematical problems and ten-bar truss are considered as numerical examples. As a result, the proposed method shows better accuracy and computational efficiency than the common RSM.

• The Journal of the Acoustical Society of Korea
• /
• v.36 no.1
• /
• pp.1-11
• /
• 2017

In this study, novel approximate form of the square-root operator of three dimensional acoustic Parabolic Equation (3D PE) is proposed using a rational approximant for two variables. This form has two advantages in comparison with existing approximation studies of the square-root operator. One is the wide-angle capability. The proposed form has wider angle accuracy to the inclination angle of ${\pm}62^{\circ}$ from the range axis of 3D PE at the bearing angle of $45^{\circ}$, which is approximately three times the angle limit of the existing 3D PE algorithm. Another is that the denominator of our approximate form can be expressed into the product of one-dimensional operators for depth and cross-range. Such a splitting form is very preferable in the numerical analysis in that the 3D PE can be easily transformed into the tridiagonal matrix equation. To confirm the capability of the proposed approximate form, comparative study of other approximation methods is conducted based on the phase error analysis, and the proposed method shows best performance.

• Journal of the Korea Society for Simulation
• /
• v.27 no.3
• /
• pp.99-107
• /
• 2018

In this paper, we study target tracking in two dimensional space using a Extended Kalman filter(EKF), various Extended Kalman Filter and Cost-Reference Particle Filter(CRPF), which can effectively estimate the state values of nonlinear measurement equation. We introduce various Extended Kalman Filter which the Unscented Kalman Filter(UKF), the Central Difference Kalman Filter(CDKF), the Square Root Unscented Kalman Filter(SR-UKF), and the Central Difference Kalman Filter(SR-CDKF). In this study, we calculate Mean Square Error(MSE) of each filters using Monte-Carlo simulation with unknown noise statistics. Simulation results show that among the various of Extended Kalman filter, Square Root Central Difference Kalman Filter has the best results in terms of speed and performance. And, the Cost-Reference Particle Filter has an advantageous feature that it does not need to know the noise distribution differently from Extended Kalman Filter, and the simulation result shows that the excellent in term of processing speed and accuracy.

• The Journal of Korea Institute of Information, Electronics, and Communication Technology
• /
• v.13 no.6
• /
• pp.568-574
• /
• 2020

In this paper, we propose a method to reduce the square root computation having high computation complexity in Canny edge detection algorithm using image processing. The proposed method is to reduce the number of operation calculating gradient magnitude using pixel's continuity using make a specific pattern instead of square root computation in gradient magnitude calculating operation. Using various test images and changing number of hole pixels, we can check for calculate match rate about 97% for one hole, and 94%, 90%, 88% when the number of hole is increased and measure decreasing computation time about 0.2ms for one hole, and 0.398ms, 0.6ms, 0.8ms when the number of hole is increased. Through this method, we expect to implement low power embedded vision system through high accuracy and a reduced operation number using two-hole pixels.

• The Journal of The Korea Institute of Intelligent Transport Systems
• /
• v.20 no.6
• /
• pp.26-36
• /
• 2021

In this study, a deep learning model for predicting the queue length was developed using the information collected from the image detector. Then, a multiple regression analysis model, a statistical technique, was derived and compared using two indices of mean absolute error(MAE) and root mean square error(RMSE). From the results of multiple regression analysis, time, day of the week, occupancy, and bus traffic were found to be statistically significant variables. Occupancy showed the most strong impact on the queue length among the variables. For the optimal deep learning model, 4 hidden layers and 6 lookback were determined, and MAE and RMSE were 6.34 and 8.99. As a result of evaluating the two models, the MAE of the multiple regression model and the deep learning model were 13.65 and 6.44, respectively, and the RMSE were 19.10 and 9.11, respectively. The deep learning model reduced the MAE by 52.8% and the RMSE by 52.3% compared to the multiple regression model.

• Communications for Statistical Applications and Methods
• /
• v.17 no.5
• /
• pp.713-724
• /
• 2010

Calculating or estimating the proper insurance premium is very important decision making process for both the policyholder and the insurance company. The credibility theory is one of the most important theories in actuarial science to get the proper premium. In this research, we introduce the rule of relative exposure volume, the square root rule and the B$\ddot{u}$hlmann credibility, and estimate the new premiums based on these methods. By real data analysis, the accuracy of these credibility methods are compared.