• Journal of applied mathematics & informatics
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• v.33 no.1_2
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• pp.61-76
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• 2015

In this paper, a fifth order extension of Potra's third order iterative method is proposed for solving nonlinear equations. A convergence theorem along with the error bounds is established. The method takes three functions and one derivative evaluations giving its efficiency index equals to 1.495. Some numerical examples are also solved and the results obtained are compared with some other existing fifth order methods. Next, the interval extension of both third and fifth order Potra's method are developed by using the concepts of interval analysis. Convergence analysis of these methods are discussed to establish their third and fifth orders respectively. A number of numerical examples are worked out using INTLAB in order to demonstrate the efficacy of the methods. The results of the proposed methods are compared with the results of the interval Newton method.

• Tribology and Lubricants
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• v.12 no.3
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• pp.115-122
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• 1996

In this paper, a finite difference method and the Newton-Raphson method are used to evaluate the Hamrock and Dowson's EHL film thickness formulas in elliptical contact problems. The minimum and central film thicknesses are compared with the Hamrock and Dowson's numerical results for various dimensionless parameters and with their film thickness formulas. The results of present analysis are more accurate and physically reasonable. The minimum film thickness formula is similar with the Hamrock and Dowson's results, however, the central film thickness formula shows large differences. Therefore, the Hamrock and Dowson's central film thickness formula should be replaced by following equation. $H_{c} = 4.88U^{0.68}G^{0.44}W^{0.096}(1-0.58e^{-0.60k})$ More accurate film thickness formula for general elliptical contact problems can be expected using present numerical methods and further research should be required.

• Proceedings of the Korean Society of Precision Engineering Conference
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• 2006.05a
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• pp.47-48
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• 2006

A roughness measuring system which comprises an integrating sphere and a stabilized laser has been fabricated with the aim of measuring the roughness correction value which is necessary in gauge block measurement by optical interferometry. To calibrate the system, a Newton's ring interferometer has been introduced. The method how to calibrate the roughness measurement system has been described.

• Proceedings of the Korean Information Science Society Conference
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• 2007.10b
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• pp.194-197
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• 2007

본 논문에서는 모바일용 3차원 그래픽 라이팅 엔진을 위한 부동소수점 멱승기클 제안한다. 3D 그래픽의 라이팅 과정은 연산량이 많고, 복잡하기 때문에 각 연산 유닛들이 저비용으로 빠르게 연산을 수행해야 한다. 본 논문에서 제안한 멱승기는 처리율을 높이기 위해 파이프라인 구조를 사용하였으며, $10^{-4}$의 정확도를 만족한다. 전체 구조는 5 stage로 구성되며, 크게 로그연산기와 지수연산기로 이루어져 있다. 일반적으로 로그연산기는 정확도를 높이기 위하여 큰 롬 테이블을 사용하는데, 이는 많은 면적을 차지하게 된다. 이러한 롬 테이블 면적 문제를 해결하기 위하여 Newton method을 사용하여 롬 테이블의 사이즈를 줄였다. 또한 오일러 상수를 밑으로 하는 지수연산기도 입력 비트의 크기를 줄이고, 테이블의 개수를 늘림으로써 롬 테이블의 크기를 줄였다. 지수연산의 밑은 부동소수점 포맷으로 [0, 1]의 범위를 가지며, 승은 정수 포맷으로 [0, 128]의 범위를 갖는다. Magnachip $0.18{\mu}m$ 공정에서 100Mhz의 동작주파수를 만족하였으며, 약 16k gates을 차지한다.

• Journal of applied mathematics & informatics
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• v.23 no.1_2
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• pp.311-319
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• 2007

This article studies a modified BFGS algorithm for solving smooth unconstrained strongly convex minimization problem. The modified BFGS method is based on the new quasi-Newton equation $B_k+1{^s}_k=yk\;where\;y_k^*=yk+A_ks_k\;and\;A_k$ is a matrix. Wei, Li and Qi [WLQ] have proven that the average performance of two of those algorithms is better than that of the classical one. In this paper, we prove the global convergence of these algorithms associated to a general line search rule.

• Transactions of the Korean Society of Automotive Engineers
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• v.4 no.4
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• pp.9-17
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• 1996

This paper develops a sequential updating method of the Euler parameter generalized coordinates for the machine kinematics and dynamics, The Newton's method is slightly modified so as to utilize the Jacobian matrix with respect to the virtual rotation instead of this with repect to the Euler parameters. An intermediate variable is introduced and the modified Newton's method solves for the variable first. Relational equation of the intermediate variable is then solved for the Euler parameters. The solution process is carried out efficiently by symoblic inversion of the relational equation of the intermediate variable and the iteration equation of the Euler parameter normalization constraint. The proposed method is applied to a kinematic and dynamic analysis with the Generalized Coordinate Partitioning method. Covergence analysis is performed to guarantee the local convergence of the proposed method. To demonstrate the validity and practicalism of the proposed method, kinematic analysis of a motion base system and dynamic analysis of a vehicle are carried out.

• Journal of Powder Materials
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• v.29 no.4
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• pp.303-308
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• 2022

The plastic deformation behavior of additively manufactured anisotropic structures are analyzed using the finite element method (FEM). Hill's quadratic anisotropic yield function is used, and a modified return-mapping method based on dual potential is presented. The plane stress biaxial loading condition is considered to investigate the number of iterations required for the convergence of the Newton-Raphson method during plastic deformation analysis. In this study, incompressible plastic deformation is considered, and the associated flow rule is assumed. The modified return-mapping method is implemented using the ABAQUS UMAT subroutine and effective in reducing the number of iterations in the Newton-Raphson method. The anisotropic tensile behavior is computed using the 3-dimensional FEM for two tensile specimens manufactured along orthogonal additive directions.

• Journal of applied mathematics & informatics
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• v.7 no.1
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• pp.237-245
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• 2000

In this paper, we consider to the adjustment weighting procedure in the two phase sampling scheme. In general, the unit nonresponses may be occured in the final survey operation. When the unit nonresponse be generated in survey, it is able to use the auxiliary variable for estimating of interest variable. In this viewpoint, we use the two kinds level of auxiliary variable, $X_{1k}$ and $X_{2k}$ for the calibration procedure. We proprose the two-step Newton's method in the calibration estimation procedure for the two phase sampling.

• Journal of the Korean Institute of Telematics and Electronics A
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• v.31A no.6
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• pp.34-44
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• 1994

In this paper, an iterative inversion method in angular spectral domain is presented for microwave imaging of a perfectly conducting cylinder. Angular spectra are calculated from measured far-field scattered fields. And then both the propagating modes and the evanescent modes are defined. The center and initial shape of an unknown conductor may be obtained by the characteristics of angular spectra and the total scattering cross section (TSCS). Finally, the orignal shape is reconstructed by the modified Newton algorithm. By using well estimated initial shape the local minima can be avoided, which might appear when the nonlinear equation is solved with Newton algorithm. It is shown to be robust to noise in scattered fields via numerical examples by keeping only the propagating modes and filtering out the evanescent modes.

• Journal of information and communication convergence engineering
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• v.10 no.1
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• pp.66-70
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• 2012

Conformal mapping has been a familiar tool of science and engineering for generations. Determination of a conformal map from the unit disk onto the Jordan region is reduced to solving the Theodorsen equation, which is an integral equation for boundary correspondence functions. There are many methods for solving the Theodorsen equation. It is the goal of numerical conformal mapping to find methods that are at once fast, accurate, and reliable. In this paper, we analyze Niethammer’s solution based on successive over-relaxation (SOR) iteration and Wegmann’s solution based on Newton iteration, and compare them to determine which one is more effective. Through several numerical experiments with these two methods, we can see that Niethammer’s method is more effective than Wegmann’s when the degree of the problem is low and Wegmann’s method is more effective than Niethammer’s when the degree of the problem is high.