• East Asian mathematical journal
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• v.28 no.5
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• pp.587-595
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• 2012

In this paper we consider the quadratic matrix equation which can be defined be $$Q(X)=AX^2+BX+C=0$$, where X is a $n{\times}n$ unknown real matrix; A,B and C are $n{\times}n$ given matrices with real elements. Newton's method is considered to find the skew-symmetric solvent of the nonlinear matrix equations Q(X). We also show that the method converges the skew-symmetric solvent even if the Fr$\acute{e}$chet derivative is singular. Finally, we give some numerical examples.

• Advances in aircraft and spacecraft science
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• v.5 no.1
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• pp.21-49
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• 2018

In this paper, geometric nonlinear bending characteristics of single wall carbon nanotube reinforced composite (SWCNTRC) doubly curved shell panels subjected to uniform transversely loadings are investigated. The nonlinear mathematical model is developed for doubly curved SWCNTRC shell panel on the basis of higher-order shear deformation theory and Green- Lagrange nonlinearity. All nonlinear higher order terms are included in the mathematical model. The effective material properties of SWCNTRC are estimated by using Eshelby-Mori-Tanaka micromechanical approach. The governing equation of the shell panel is obtained using the total potential energy principle and a Newton-Raphson iterative method is employed to compute the nonlinear displacement and stresses. The present results are compared with published literature. The effect of SWCNT volume fraction, width-to-thickness ratio, radius-to-width ratio (R/a), boundary condition, linear and nonlinear deflection, stresses and different types of shell geometry on nonlinear bending response is investigated.

• Journal of the Korean Institute of Telematics and Electronics B
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• v.33B no.4
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• pp.91-99
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• 1996

A hybrid approach employing both the genetic algorithm and the newton-raphson method is proposed for the electrical impedance computed tomography (EICT) image reconstruction. Computational experiments based on the new concept have shown promising results for several noise-free models. In particular, the resistance distribution of the tested models having resistivity ratio up to 100:1 has been reconstructed sucessfully. Using the proposed mehtod, it is also possible to get the reconstruction by the conventional iterative approaches be difficult to vonverge to a robust solution. If the compution power is enhanced further, the proposed method is expected to stimulate the practical applications of the EICT technology in the near future.

• Proceedings of the Korean Society for Noise and Vibration Engineering Conference
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• 2000.06a
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• pp.144-150
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• 2000

In this paper, we introduce a modified six-degrees-of-freedom parallel-link manipulator, which will be applied to the human vibration experiments. We analyze the inverse kinematics and workspace of this manipulator and comprehend the characteristics of kinematics analyzed. Additionally, solutions of forward kinematics are obtained through the iterative Newton-Raphson method known as one of the most used numerical analysis. Finally, dynamic equation of the manipulator is derived in closed form through the Newton-Euler approach, which will be used for the development of control software.

• Journal of the Korean Mathematical Society
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• v.57 no.4
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• pp.915-933
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• 2020

A two-level finite element method based on the Newton iterative method is proposed for solving the Navier-Stokes/Darcy model. The algorithm solves a nonlinear system on a coarse mesh H and two linearized problems of different loads on a fine mesh h = O(H^4-𝜖). Compared with the common two-grid finite element methods for the considered problem, the presented two-level method allows for larger scaling between the coarse and fine meshes. Moreover, we prove the stability and convergence of the considered two-level method. Finally, we provide numerical experiment to exhibit the effectiveness of the presented method.

• Journal of the Korean Statistical Society
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• v.27 no.2
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• pp.165-187
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• 1998

Shin and Sarkar (1993, 1994) studied the problem of testing for a unit root in an AR(p) signal observed with MA(q) noise when the MA parameters are known. In this paper we consider the case when the MA parameters are unknown and to be estimated. Test statistics are defined using unit root parameter estimates based on three different estimation methods of Hannan and Rissanen (1982), Kohn (1979) and Shin and Sarkar (1995). An AR(p) process contaminated by MA(q) noise is a .estricted ARMA model, for which Shin and Sarkar (1995) derived an easy-to-compute Newton- Raphson estimator The two-stage estimation p.ocedu.e of Hannan and Rissanen (1982) is used to compute initial parameter estimates in implementing the iterative estimation methods of both Shin and Sarkar (1995) and Kohn (1979). In a simulation study we compare the relative performance of these unit root tests with respect to both size and power for p=q=1.

• Journal of the Korean Mathematical Society
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• v.53 no.4
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• pp.781-793
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• 2016

The solutions of equations are usually found using iterative methods whose convergence order is determined by Taylor expansions. In particular, the local convergence of the method we study in this paper is shown under hypotheses reaching the third derivative of the operator involved. These hypotheses limit the applicability of the method. In our study we show convergence of the method using only the first derivative. This way we expand the applicability of the method. Numerical examples show the applicability of our results in cases earlier results cannot.

• Proceedings of the KIEE Conference
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• 1997.11a
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• pp.231-234
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• 1997

This paper presents improved direct method for calculating the closest saddle node bifurcation (CSNB) point, which is also applicable to the selection of appropriate load shedding, reactive power compensation point detection. The proposed method reduced dimension of nonlinear equation compared with that of Dobson's direct method. The improved direct method, utilizing Newton Iterative method converges very quickly. But it diverges if the initial guess is not very close to CSNB. So the direct method is performed with the initial values obtained by carrying out the iterative method twice, which is considered most efficient at this time. Since sparsity techniques can be employed, this method is a good choice to a large scale system on-line application. Proposed method has been tested for 5-bus, New England 30-bus system.

• Kyungpook Mathematical Journal
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• v.62 no.4
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• pp.699-713
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• 2022

This paper proposes a hybrid successive over-relaxation iterative method for the numerical solution of a nonlinear diffusion in a one-dimensional porous medium. The considered mathematical model is discretized using a computational complexity reduction scheme called half-sweep finite differences. The local truncation error and the analysis of the stability of the scheme are discussed. The proposed iterative method, which uses explicit group technique and modified successive over-relaxation, is formulated systematically. This method improves the efficiency of obtaining the solution in terms of total iterations and program elapsed time. The accuracy of the proposed method, which is measured using the magnitude of absolute errors, is promising. Numerical convergence tests of the proposed method are also provided. Some numerical experiments are delivered using initial-boundary value problems to show the superiority of the proposed method against some existing numerical methods.

• Journal of Korean Society of Industrial and Systems Engineering
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• v.4 no.5
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• pp.11-14
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• 1981

This study intends to decide the economic sample size based on the cost of sampling Inspection for destructive testing. The marginal percent defective is used as the lot tolerance percent defective (LTPD), and the Newton's iterative method is adopted to calculate the optimum sample size(n), given by the consumer's risk($\beta$ - risk) and the acceptance number(c).