• 한국정밀공학회:학술대회논문집
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• 한국정밀공학회 2004년도 추계학술대회 논문집
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• pp.347-350
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• 2004

In this paper, the acceleration is studied for the rigid-plastic FEM of metal forming simulation. In the FEM, the direct iteration and Newton-Raphson iteration are applied to obtain the initial solution and accurate solution respectively. In general, the acceleration scheme for the direct iteration is not used. In this paper, an Aitken accelerator is applied to the direct iteration. In the modified Newton-Raphson iteration, the step length or the deceleration coefficient is used for the fast and robust convergence. The step length can be determined by using the accelerator. The numerical experiments have been performed for the comparisons. The faster convergence is obtained with the acceleration in the direct and Newton-Raphson iterations.

• 대한수학회지
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• 제55권6호
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• pp.1529-1540
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• 2018

The matrix equation $X^p+A^*XA=Q$ has been studied to find the positive definite solution in several researches. In this paper, we consider fixed-point iteration and Newton's method for finding the matrix p-th root. From these two considerations, we will use the Newton-Schulz algorithm (N.S.A). We will show the residual relation and the local convergence of the fixed-point iteration. The local convergence guarantees the convergence of N.S.A. We also show numerical experiments and easily check that the N.S. algorithm reduce the CPU-time significantly.

• East Asian mathematical journal
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• 제29권5호
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• pp.511-519
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• 2013

There are various methods for evaluating a matrix square root, which is a solvent of the quadratic matrix equation $X^2-A=0$. We consider new iterative methods for solving matrix square roots of M-matrices. Particulary we show that the relaxed binomial iteration is more efficient than Newton-Schulz iteration in some cases. And we construct a formula to find relaxation coefficients through statistical experiments.

• 대한수학회보
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• 제53권6호
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• pp.1831-1844
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• 2016

In this paper, we improve the full-Newton step infeasible interior-point algorithm proposed by Mansouri et al. [6]. The algorithm takes only one full-Newton step in a major iteration. To perform this step, the algorithm adopts the largest logical value for the barrier update parameter ${\theta}$. This value is adapted with the value of proximity function ${\delta}$ related to (x, y, s) in current iteration of the algorithm. We derive a suitable interval to change the parameter ${\theta}$ from iteration to iteration. This leads to more flexibilities in the algorithm, compared to the situation that ${\theta}$ takes a default fixed value.

• 한국분말재료학회지
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• 제30권1호
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• pp.29-34
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• 2023

A fixed-point iteration is proposed to integrate the stress and state variables in the incremental analysis of plastic deformation. The Conventional Newton-Raphson method requires a second-order derivative of the yield function to generate a complicated code, and the convergence cannot be guaranteed beforehand. The proposed fixed-point iteration does not require a second-order derivative of the yield function, and convergence is ensured for a given strain increment. The fixed-point iteration is easier to implement, and the computational time is shortened compared with the Newton-Raphson method. The plane-stress condition is considered for the biaxial loading conditions to confirm the convergence of the fixed-point iteration. 3-dimensional tensile specimen is considered to compare the computational times in the ABAQUS/explicit finite element analysis.

• 한국전자파학회논문지
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• 제28권11호
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• pp.880-885
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• 2017

기존에 제안된 AD-MUSIC 알고리즘을 이용하여 2차원 탐색 없이 1차원 탐색을 반복함으로써 DOD/DOA 추정이 가능하다. 본 논문에서는 계산량을 더욱 감소하기 위해 1차원 탐색에 Newton 기반 기법을 적용한다. 본 논문은 바이스태틱 MIMO 레이다 시스템의 수신신호 모델링과 AD-MUSIC의 유도과정을 보이고, 뉴턴 반복 기법을 AD-MUSIC에 적용한다. 추정 시, 기존의 AD-MUSIC 알고리즘의 성능과 계산량이 탐색 간격에 영향을 받는 것에 반해, AD-MUSIC의 성능과 뉴턴기법을 적용하는 본 논문의 방법인 경우, 탐색 간격에 관계없이 우수한 성능을 보이고, 계산량 또한 감소하는 효과를 보인다는 것을 시뮬레이션을 통해 보인다.

• Korean Journal of Mathematics
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• 제9권1호
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• pp.67-73
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• 2001

For some equation related with exponential function, we seek roots and find the properties of the roots. By using the relation of the roots and attractors, we find a region in the basin of attraction of the attractor at infinity for Newton's method for solving given equation.

• East Asian mathematical journal
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• 제35권3호
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• pp.341-349
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• 2019

In this paper, we are concerned with the minimal positive solution to system of the nonlinear matrix equations $A_1X^2+B_1Y +C_1=0$ and $A_2Y^2+B_2X+C_2=0$, where $A_i$ is a positive matrix or a nonnegative irreducible matrix, $C_i$ is a nonnegative matrix and $-B_i$ is a nonsingular M-matrix for i = 1, 2. We apply Newton's method to system and present a modified Newton's iteration which is validated to be efficient in the numerical experiments. We prove that the sequences generated by the modified Newton's iteration converge to the minimal positive solution to system of nonlinear matrix equations.

• 한국공간구조학회:학술대회논문집
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• 한국공간구조학회 2006년도 춘계 학술발표회 논문집 제3권1호(통권3호)
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• pp.170-174
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• 2006

This paper presents a new nonlinear analysis algorithm which uses the equivalent nodal load for the element stiffness. The equivalent nodal load represents the influence of the stiffness change such as the addition of elements, the deletion of elements, and/or the partial change of element stiffness. The nonlinear analysis of structures using the equivalent load improves the efficiency very much because the inverse of the structural stiffness matrix, which needs a large amount of computation to calculate, is reused in each loading step. In this paper, the concept of nonlinear analysis using the equivalent load for the element stiffness is described and some numerical examples are provided to verify it.

• 전산구조공학
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• 제11권1호
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• pp.205-216
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• 1998

본 논문에서는 중복근을 갖는 비비례 감쇠시스템의 고유치 해석 방법을 제안하였다. 2차 고유치 문제의 행렬 조합을 통한 선형 방정식에 수정된 Newton-Raphson기법과 고유벡터의 직교성을 적용하여 제안방법의 알고리즘을 유도하였다. 벡터 반복법 또는 부분공간 반복법과 같은 기존의 반복법에서는 수렴성을 향상시키기 위해 변위법을 적용하였으며, 이 값이 시스템의 고유치에 근사하게 되면 행렬분해 과정에서 특이성이 발생한다. 그러나 제안방법은 구하고자 하는 고유치가 중복근이 아닐 경우에, 변위값이 시스템의 고유치 일지라도 항상 정칙성을 유지하며, 이것을 해석적으로 증명하였다. 제안방법은 수정된 Newton-Raphson기법을 이용하기 때문에 초기값을 필요로 한다. 제안방법의 초기값으로는 반복법의 중간결과나 근사법의 결과를 사용할 수 있다. 이들 방법중 Lanczon방법이 가장 효율적으로 좋은 초기값을 제공하기 때문에 Lanczon방법의 결과를 제안방법의 초기값으로 사용하였다. 제안방법의 효율성을 증명하기 위하여 두가지 예제 구조물에 대해 해석시간 및 수렴성을 가장 많이 사용하고 있는 부분공간 반복법과 Lanczon방법의 결과와 비교하였다.