• 대한수학회논문집
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• 제13권1호
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• pp.195-209
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• 1998

In this paper we present a new iteration method for solving optimization problems governed by partial differential equations. We generalize the existing methods such as simple gradient methods and pseudo-time methods to get an efficient iteration method. Numerical tests show that the convergence of the new iteration method is much faster than those of the pseudo-time methods especially when the parameter $\sigma$ in the cost functional is small.

• 한국정보통신학회:학술대회논문집
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• 한국해양정보통신학회 2003년도 춘계종합학술대회
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• pp.753-757
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• 2003

본 논문에서는 반복복호 부호의 복호과정시 채널 적응적으로 반복복호수를 가변할 수 있는 효율적인 제어기법을 제안한다. 반복복호 부호는 반복구조를 가지며 그 특성상 반복복호수가 증가할수록 성능이 우수하게 향상된다. 그러나 반복복호수가 증가한 수록 복호과정시 적용된 알고리즘의 복잡도에 따라 다소 차이는 있지만 공통적으로 계산량의 증가를 가지게 되며 이는 복호지연시간 증가로 나타난다. 또한 일정 반복복호수 이상에 도달하게 되면 그 성능 변화가 거의 없는 오류마구(floor) 현상이 나타난다. 즉 성능변화가 없는 적절한 반복복호수 종료점을 찾아야 한다. 따라서 본 논문에서는 프레임 주기로 수신된 정보를 프레임 에러체크 지시자를 이용하여 채널의 변화를 감시하며 반복복호 부호의 반복복호수를 채널 적응적으로 승가, 감소할 수 있도록 제어하는 기법을 제안하였으며 결과적으로 반복구조를 가지는 부호의 방대한 계산량 감소와 이로 인한 복호지연 시간을 성능저하없이 효율적으로 단축시킬 수 있음을 보였다.

• Journal of the Korean Society for Industrial and Applied Mathematics
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• 제14권1호
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• pp.29-34
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• 2010

The QR method is one of the most common methods for calculating the eigenvalues of a square matrix, however its understanding would require complicated and sophisticated mathematical logics. In this article, we present a simple way to understand QR method only with a minimal mathematical knowledge. A deflation technique is introduced, and its combination with the power iteration leads to extracting all the eigenvectors. The orthogonal iteration is then shown to be compatible with the combination of deflation and power iteration. The connection of QR method to orthogonal iteration is then briefly reviewed. Our presentation is unique and easy to understand among many accounts for the QR method by introducing the orthogonal iteration in terms of deflation and power iteration.

• 한국소음진동공학회논문집
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• 제15권1호
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• pp.112-117
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• 2005

Two modified versions of subspace iteration method using accelerated starting vectors are proposed to efficiently calculate free vibration modes of structures. Proposed methods employ accelerated Lanczos vectors as starting iteration vectors in order to accelerate the convergence of the subspace iteration method. Proposed methods are divided into two forms according to the number of starting vectors. The first method composes 2p starting vectors when the number of required modes is p and the second method uses 1.5p starting vectors. To investigate the efficiency of proposed methods, two numerical examples are presented.

• 대한수학회보
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• 제37권1호
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• pp.153-169
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• 2000

Let E be a real q-uniformly smooth Banach space which admits a weakly sequentially continuous duality map, and K a nonempty closed convex subset of E. Let T : K -> K be a mapping such that $F(T)\;=\;{x\;{\in}\;K\;:\;Tx\;=\;x}\;{\neq}\;0$ and (I - T) satisfies the accretive-type condition: $\;{\geq}\;{\lambda}$\mid$$\mid$x-Tx$\mid$$\mid$^2$, for all $x\;{\in}\;K,\;x^*\;{\in}\;F(T)$ and for some ${\lambda}\;>\;0$. The weak and strong convergence of the Ishikawa iteration method to a fixed point of T are investigated. An application of our results to the approximation of a solution of a certain linear operator equation is also given. Our results extend several important known results from the Mann iteration method to the Ishikawa iteration method. In particular, our results resolve in the affirmative an open problem posed by Naimpally and Singh (J. Math. Anal. Appl. 96 (1983), 437-446).

• 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.

• East Asian mathematical journal
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• 제18권2호
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• pp.261-270
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• 2002

We obtain the convergence of three-step iteration methods and generalized three-step iteration methods for quasi-contractive and generalized quasi-contractive mappings, respectively, in Banach spaces. Our results extend the corresponding results in [1], [4]-[6].

• 한국소음진동공학회:학술대회논문집
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• 한국소음진동공학회 2004년도 추계학술대회논문집
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• pp.717-720
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• 2004

Two modified versions of subspace iteration method using accelerated starting vectors are proposed to efficiently calculate free vibration modes of structures. Proposed methods employ accelerated Lanczos vectors as starting iteration vectors in the subspace iteration method. To investigate the efficiency of proposed methods, two numerical examples are presented.

• 대한전기학회:학술대회논문집
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• 대한전기학회 1996년도 추계학술대회 논문집 학회본부
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• pp.179-181
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• 1996

In conventional hydrothermal coordination problem, the lambda-gamma iteration method is generally used for generation schedule. The procedure of classical lambda-gamma iteration method consists of 3 main loops and it is very complex. Therefore, it needs many iterative calculations. This paper proposes an advanced hydrothermal algorithm based on newly developed lambda-gamma iteration method. As lambda calculation loop is removed in the newly developed iteration method, iterative calculations are reduced and whole procedure is simplified. The proposed algorithm is verified on simple system.

• Journal of applied mathematics & informatics
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• 제29권1_2호
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• pp.381-394
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• 2011

In this paper, a Naveir-Stokes equation is solved by using the Adomian's decomposition method (ADM), modified Adomian's decomposition method (MADM), variational iteration method (VIM), modified variational iteration method (MVIM), modified homotopy perturbation method (MHPM) and homotopy analysis method (HAM). The approximate solution of this equation is calculated in the form of series which its components are computed by applying a recursive relation. The existence and uniqueness of the solution and the convergence of the proposed methods are proved. A numerical example is studied to demonstrate the accuracy of the presented methods.