• Journal of applied mathematics & informatics
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• 제4권1호
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• pp.83-108
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• 1997

Chebysheff-Halley methods are probably the best known cubically convergent iterative procedures for solving nonlinear equa-tions. These methods however require an evaluation of the second Frechet-derivative at each step which means a number of function eval-uations proportional to the cube of the dimension of the space. To re-duce the computational cost we replace the second Frechet derivative with a fixed bounded bilinear operator. Using the majorant method and Newton-Kantorovich type hypotheses we provide sufficient condi-tions for the convergence of our method to a locally unique solution of a nonlinear equation in Banach space. Our method is shown to be faster than Newton's method under the same computational cost. Finally we apply our results to solve nonlinear integral equations appearing in radiative transfer in connection with the problem of determination of the angular distribution of the radiant-flux emerging from a plane radiation field.

• 대한토목학회논문집
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• 제14권5호
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• pp.1105-1113
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• 1994

각종 구조물의 설계에 있어서 동적해석은 필수적이다. 이러한 구조물의 동적해석에 모우드 중첩법을 사용할 경우 고유치문제의 해석이 선행되어야 한다. 그러나 동적해석에 있어서 대부분의 노력, 즉 시간은 고유치와 그에 대응하는 고유벡터를 구하기 위하여 사용되기 때문에 보다 효율적인 고유치해법의 개발이 요구된다. 본 논문은 수치적 불안정성을 해소하고 수렴성을 향상시킴으로써 전체 해석시간을 줄이기 위해 Robinson-Lee 방법에 accelerated Newton-Raphson 방법을 적용한 고유치해법을 제시하였다. 제안방법의 효율성은 몇가지의 수치해석을 통해서 증명하였다.

• 전기의세계
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• 제26권2호
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• pp.78-83
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• 1977

The Newton-Raphson method has now gained widespread popularity in Load-flow calculationes. In this paper programming is developed with aims to improve the convergence characteristics, speed and memory requirements in the above method. The method of Load-flow calculations is performed by employing the MW-O/MVAR-V decoupling principle. To reduce the memory requirements and improve the speed of calculation the programming of the Optimally Ordered Triangular Factorization method is developed. Besides this, other measures are taken to reduce memory requirements and computing time and to improve reliability. KECO'S 48 Bus system was tested and the method suggested in this paper was proved to be faster than any other methods.

• 한국전산유체공학회:학술대회논문집
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• 한국전산유체공학회 1998년도 추계 학술대회논문집
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• pp.153-159
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• 1998

The Newton-Krylov method on the unstructured grid flow solver using the cell-centered spatial discretization oi compressible Euler equations is presented. This flow solver uses the reconstructed primitive variables to get the higher order solutions. To get the quadratic convergence of Newton method with this solver, the careful linearization of face flux is performed with the reconstructed flow variables. The GMRES method is used to solve large sparse matrix and to improve the performance ILU preconditioner is adopted and vectorized with level scheduling algorithm. To get the quadratic convergence with the higher order schemes and to reduce the memory storage. the matrix-free implementation and Barth's matrix-vector method are implemented and compared with the traditional matrix-vector method. The convergence and computing times are compared with each other.

• 대한전기학회:학술대회논문집
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• 대한전기학회 1998년도 추계학술대회 논문집 학회본부A
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• pp.311-315
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• 1998

Load Flow calculation methods can usually be divided into Gauss-Seidel method, Newton-Raphson method and decoupled method. Load flow calculation is a basic on-line or off-line process for power system planning, operation, control and state analysis. These days Newton-Raphson method is mainly used since it shows remarkable convergence characteristics. It, however, needs considerable calculation time in construction and calculation of inverse Jacobian matrix. In addition to that, Newton-Raphson method tends to fail to converge when system loading is heavy and system has a large R/X ratio. In this paper, matrix equation is used to make algebraic expression and then to solve load flow equation and to modify above defects. And it preserve certain part of Jacobian matrix to shorten the time of calculation. Application of mentioned algorithm to 14 bus, 39 bus, 118 bus systems led to identical result and the number of iteration got by Newton-Raphson method. The effect of time reduction showed about 28%, 30%, at each case of 39 bus, 118 bus system.

• Journal of applied mathematics & informatics
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• 제27권5_6호
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• pp.1195-1209
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• 2009

In this paper, we point out some errors in a recent paper by Cordero and Torregrosa [7]. We prove the convergence of the variants of Newton's method for solving the system of nonlinear equations using two different approaches. Several examples are given, which illustrate the cubic convergence of these methods and verify the theoretical results.

• Journal of applied mathematics & informatics
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• 제7권1호
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• pp.29-40
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• 2000

We provide semilocal convergence theorems for Newton-like methods in Banach space using outer and generalized inverses. In contrast to earlier results we use hypotheses on the second instead of the first Frechet-derivative. This way our Newton-Kantorovich hypotheses differ from earlier ones. Our results can be used to solve undetermined systems, nonlinear least square problems and ill-posed nonlinear operator equations.

• East Asian mathematical journal
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• 제27권5호
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• pp.521-525
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• 2011

We use a weaker version of the celebrated Newton-Kantorovich theorem [3] reported by us in [1] to find solutions of discrete dynamical systems involving operators with chaotic behavior. Our results are obtained by extending the application of the shadowing lemma [4], and are given under the same computational cost as before [4]-[6].

• 조명전기설비학회논문지
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• 제29권9호
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• pp.71-80
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• 2015

This paper proposes a convenient thermal modeling method for loss distribution control method of 3-level Active NPC(Neutral Point Clamped) inverter. In the drawback of conventional 3-level NPC, the generated losses can occur unbalance in each switching device, as a result, thermal utilization of designed system has been decreased. In order to compensate unbalanced losses, Active NPC inverter performed loss balancing control with thermal modeling during operation of each switching device. Therefore, this paper deals with a convenient thermal modeling method based on newton's law of cooling rather than conventional thermal modeling method. Both simulation and experimental results based on 10kW 3-level Active NPC inverter confirm the validity of the analysis performed in the study.

• 한국해양공학회지
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• 제37권6호
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• pp.256-265
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• 2023

Many numerical methods have been developed since 1961, but unresolved issues remain. This study developed a numerical method to address these issues and determine the coefficients and properties of rotational waves with a shear current in a finite water depth. The number of unknown constants was reduced significantly by introducing a wavelength-independent coordinate system. The reference depth was calculated independently using the shooting method. Therefore, there was no need for partial derivatives with respect to the wavelength and the reference depth, which simplified the numerical formulation. This method had less than half of the unknown constants of the other method because Newton's method only determines the coefficients. The breaking limit was calculated for verification, and the result agreed with the Miche formula. The water particle velocities were calculated, and the results were consistent with the experimental data. Dispersion relations were calculated, and the results are consistent with other numerical findings. The convergence of this method was examined. Although the required series order was reduced significantly, the total error was smaller, with a faster convergence speed.