• 대한수학회지
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• 제58권3호
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• pp.525-552
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• 2021

In this paper, we introduce two general iterative algorithms (one implicit algorithm and one explicit algorithm) for finding a common element of the solution set of the variational inequality problems for a continuous monotone mapping, the zero point set of a set-valued maximal monotone operator, and the fixed point set of a continuous pseudocontractive mapping in a Hilbert space. Then we establish strong convergence of the proposed iterative algorithms to a common point of three sets, which is a solution of a certain variational inequality. Further, we find the minimum-norm element in common set of three sets.

• 대한기계학회논문집A
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• 제24권5호
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• pp.1215-1230
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• 2000

Parallel Approaches using Cray T3E which is NIPP (Massively Parallel Processors) machine are presented for the efficient computation of the finite element analysis of 3-D shape rolling processes. D omain decomposition method coupled with parallel linear equation solver is used. Domain decomposition is applied for obtaining element tangent stifffiess matrices and residual vectors. Direct and iterative parallel algorithms are used for solving the linear equations. Direct algorithm is_parallel version of direct banded matrix solver. For iterative algorithms, the well-known preconditioned conjugate gradient solver with Jacobi preconditioner is also employed. Moreover a new effective iterative scheme with block inverse matrix preconditioner, which is named by present authors, is presented and its results are compared with the one using Jacobi preconditioner. PVM and MPI are used for message passing and synchronization between processors. The performance and efficiency of each algorithm is discussed and comparisons are made among different algorithms.

• 대한전자공학회논문지TC
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• 제42권7호
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• pp.27-34
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• 2005

Iterative detection은 additive white Gaussian noise(AWGN) channel의 경우 interleaver들을 포함한 조합유한상태머신(concatenated Finite State Machine)들에 대해 근사적으로 optimal solution에 가깝다는 것이 입증되었습니다. 수신단에서 정확한 채널 상태 정보(perfect channel state information)가 얻어질 수 없는 경우 adaptive Iterative detection이 시간적으로 변하거나 또는 부정확한 채널 변수를 다루기위해 필요합니다. Iterative detection과 adaptive iterative detection대한 기본 building block은 각각 Soft-Input Soft-Output (SISO)와adaptive SISO (A-SISO)입니다. SISO와 A-SISO의 complexity은 state memory나 channel memory에 비례해서 지수적으로 증가합니다. 본 논문에서는 Reduced State SISO (RS-SISO) 알고리즘이 A-SISO의 complexity 감소를 위해 적용되어 fading ISI channel을 통한 serially concatenated CPM의 성능이 adaptive iterative detection을 이용하면 터보 코드 같은 성능을 나타내는 것과 또한 RS-A-SISO system이 큰 iterative detection gain을 가지는 것을 보였습니다. RS-A-SISO 알고리즘에 대한 다양한 design option들의 성능을 평가하였으며 성능과 complexity를 비교하였습니다. 또한 보통 AWGN 채널에서 사용되어지는 density evolution 분석기법이 주파수 선택적인 페이딩 채널에서 RS-A-SISO 시스템에서도 좋은 분석기법임을 보였습니다

• East Asian mathematical journal
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• 제17권1호
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• pp.57-70
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• 2001

In this paper, we introduce a class of generalized quasivariational inclusions for fuzzy mappings and show its equivalence with a class of fixed point problems. Using this equivalence, we develop the Mann and Ishikawa type perturbed iterative algorithms for this class of generalized quasivariational inclusions. Further, we prove the existence of solutions for the class of generalized quasivariational inclusions and discuss the convergence criteria for the perturbed algorithms.

• Korean Journal of Mathematics
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• 제13권1호
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• pp.113-122
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• 2005

We consider the iterative schemes for the large sparse linear system to solve partial differential equations. Using spectral radius of iteration matrices, the optimal relaxation parameters and good parameters can be obtained. With those parameters we compare the effectiveness of the SOR and SSOR algorithms. Applying Crank-Nicolson approximation, we observe the error distribution according to domain decomposition. The number of processors due to domain decomposition affects time and error. Numerical experiments show that effectiveness of SOR and SSOR can be reversed as time size varies, which is not the usual case. Finally, these phenomena suggest conjectures about equilibrium time grid for SOR and SSOR.

• Journal of applied mathematics & informatics
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• 제5권2호
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• pp.357-372
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• 1998

In this paper we introduce and study a new class of random completely generalized strongly nonlinear quasi -comple- mentarity problems with non-compact valued random fuzzy map-pings and construct some new iterative algorithms for this kind of random fuzzy quasi-complementarity problems. We also prove the existence of random solutions for this class of random fuzzy quasi-complementarity problems and the convergence of random iterative sequences generated by the algorithms.

• 대한수학회지
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• 제57권3호
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• pp.617-640
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• 2020

In this paper, we introduce a parallel iterative method for finding a common fixed point of a finite family of Bregman strongly nonexpansive mappings in a real reflexive Banach space. Moreover, we give some applications of the main theorem for solving some related problems. Finally, some numerical examples are developed to illustrate the behavior of the new algorithms with respect to existing algorithms.

• East Asian mathematical journal
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• 제18권1호
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• pp.95-109
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• 2002

In this paper, we study a class of variational inequalities, which is called the generalized set-valued mixed variational inequality. By using the properties of the resolvent operator associated with a maximal monotone mapping in Hilbert spaces, we have established an existence theorem of solutions for generalized set-valued mixed variational inequalities, suggesting a new iterative algorithm and a perturbed proximal point algorithm for finding approximate solutions which strongly converge to the exact solution of the generalized set-valued mixed variational inequalities.

• 한국항해학회지
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• 제14권4호
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• pp.31-39
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• 1990

A systematic methodology for efficient implementation of processor arrays from regular iterative algorithms is proposed. One of the modern parallel processing array architectures is the Systolic arrays and we use it for processor arrays on this paper. On designing the systolic arrays, there are plenty of mapping functions which satisfy necessary conditions for its implementation to the time-space domain. In this paper, we sue a few conditions to reduce the total number of computable mapping functions efficiently. As a results of applying this methodology, efficient designs of systolic arrays could be done with considerable saving on design time and efforts.

• Journal of applied mathematics & informatics
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• 제28권1_2호
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• pp.75-86
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• 2010

An iterative algorithm was been studied which can be viewed as an extension of the previously known algorithms for asymptotically nonexpansive mappings. Subsequently, we study the convergence problem of the proposed iterative algorithm for asymptotically nonexpansive mappings under some mild conditions in Banach spaces.