• Journal of the Korean Society for Industrial and Applied Mathematics
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• v.15 no.1
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• pp.19-30
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• 2011

In [21], we compared the Newton-Krylov method and some high-order methods to solve nonlinear systems. In this paper, we propose high-order Newton-Krylov methods combining the Newton-Krylov method with some high-order iterative methods to solve systems of nonlinear equations. We provide some numerical experiments including comparisons of CPU time and iteration numbers of the proposed high-order Newton-Krylov methods for several nonlinear systems.

• IEMEK Journal of Embedded Systems and Applications
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• v.9 no.5
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• pp.285-292
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• 2014

The commonly used Newton-Raphson's floating-point number divider algorithm performs two multiplications in one iteration. In this paper, a tentative K'th Newton-Raphson's floating-point number divider algorithm which performs K times multiplications in one iteration is proposed. Since the number of multiplications performed by the proposed algorithm is dependent on the input values, the average number of multiplications per an operation in single precision and double precision divider is derived from many reciprocal tables with varying sizes. In addition, an error correction algorithm, which consists of one multiplication and a decision, to get exact result in divider is proposed. 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 divider unit. Also, it can be used to construct optimized approximate reciprocal tables.

• IEMEK Journal of Embedded Systems and Applications
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• v.13 no.1
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• pp.45-51
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• 2018

In this paper, a tentative Kth order Newton-Raphson's floating point number Nth root algorithm for K order convergence rate in one iteration is proposed by applying Taylor series to the Newton-Raphson root algorithm. Using the proposed algorithm, $F^{-1/N}$ and $F^{-(N-1)/N}$ can be computed from iterative multiplications without division. It also predicts the error of the algorithm iteration and iterates only 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.

• The Pure and Applied Mathematics
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• v.15 no.1
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• pp.47-55
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• 2008

Local convergence results for three Newton-like methods in Banach space are provided. A comparison is given between the three convergence radii. Then we show that using the largest convergence radius we can pick an initial guess from with we start the corresponding iteration. It turns out that after a finite number of steps we can always use the iterate found as the starting guess for a faster method, since this iterate will be inside the convergence domain of the new method.

• Journal of applied mathematics & informatics
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• v.29 no.3_4
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• pp.909-920
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• 2011

A regularized Newton method for nonlinear ill-posed problems is considered. In each Newton step an implicit iterative method with an appropriate stopping rule is proposed and analyzed. Under certain assumptions on the nonlinear operator, the convergence of the algorithm is proved and the algorithm is stable if the discrepancy principle is used to terminate the outer iteration. Numerical experiment shows the effectiveness of the method.

• Journal of the Society of Naval Architects of Korea
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• v.45 no.4
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• pp.389-395
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• 2008

It is very well known that the natural frequency of an oscillating body on the free surface is determinable only after the added mass is given. However, it is hard to find analytical investigations in which actually the natural frequency is obtained. Difficulties arise from the fact that in order to determine the natural frequency we need to compute the added mass at least for a range of frequencies, and to solve an equation where the frequency is a variable. In this study, first, a formula is obtained for the added mass, and then an equation for finding the natural frequency is defined and solved by Newton's iteration. It is confirmed that the formula shows a good agreement with the results given by Ursell(1949), and the value of natural frequency is reduced by 21.5% compared to the pre-natural frequency, which is obtained without considering the effect of added mass.

• Proceedings of the ESK Conference
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• 1997.10a
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• pp.463-467
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• 1997

인간에게 운동감을 적절히 제시해주기 위하여는 Newton에 의한 운동의 세가지 법칙뿐만 아니라 EInstein의 상대성이론이 첨가되어야 한다. 즉, Newton운동의 제1법칙에 의하여 피실험자가 외력을 받지 않으면 등속운동 또는 정지상태를 계속 유지하게 되어 자신이 등속좌표계에 고정되어있기 때문에 시각적 인 정보가 없으면 어떠한 운동감도 못 느낀다. 이때 피실험자에게 정지해있는 기준좌표계에 대하여 등속 으로 움직이는 것을 인식시켜주기 위하여 피실험자에 대한 기준좌표계의 상대속도를 시각정보로 제공해 주어야 한다. 또한 Newton운동의 제2법칙에 의하여 똑같은 힘이 외력으로 작용하더라도 피실험자의 질량과 가속도는 서로 반비례하므로 화면이동속도변화를 피실험자의 질량에 반비례하도록 제시해 주어야 한다(김 정흠, 1982). 본 연구에서는 이러한 개념에 근거하여, 체중이 다른 여섯 피실험자들로 구성된 시스템에 대해서 각 피실험자에게 서로 다른 변위를 주고자할 때, 여섯가지 외력에 요구되는 작용시간을 Jacobi Iteration 방법과 Gauss-Seidel Iteration 방법으로 구하는 알고리즘을 제시하였다(D.V. Griffiths and I.M. Smith, 1991).

• 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.

• Proceedings of the Earthquake Engineering Society of Korea Conference
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• 2003.03a
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• pp.481-490
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• 2003

This paper presents an efficient eigensolution method for non-proportionally damped systems. The proposed method is obtained by applying the accelerated Newton-Raphson technique and the orthonormal condition of the eigenvectors to the linearized form of the quadratic eigenproblem. A step length and a selective scheme are introduced to increase the convergence of the solution. The step length can be evaluated by minimizing the norm of the residual vector using the least square method. While the singularity may occur during factorizing process in other iteration methods such as the inverse iteration method and the subspace iteration method if the shift value is close to an exact eigenvalue, the proposed method guarantees the nonsingularity by introducing the orthonormal condition of the eigenvectors, which can be proved analytically. A numerical example is presented to demonstrate the effectiveness of the proposed method.

• Journal of applied mathematics & informatics
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• v.29 no.1_2
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• pp.119-133
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• 2011

This paper proposes an infeasible interior-point algorithm with full-Newton step for linear programming. We introduce a special self-regular proximity to induce the feasibility step and also to measure proximity to the central path. The result of polynomial complexity coincides with the best-known iteration bound for infeasible interior-point methods, namely, O(n log n/${\varepsilon}$).