• Communications of the Korean Mathematical Society
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• v.22 no.2
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• pp.247-258
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• 2007

In this paper a new class of system of generalized nonlinear variational inequalities involving strongly monotone, relaxed co coercive and relaxed generalized monotone mappings in Hilbert spaces is introduced and studied. Based on the projection method, an equivalence between the system of generalized nonlinear variational inequalities and the fixed point problem is established, which is used to suggest some new iterative algorithms for computing approximate solutions of the system of generalized nonlinear variational inequalities. A few sufficient conditions which ensure the existence and uniqueness of solution of the system of generalized nonlinear variational inequalities are given, and the convergence analysis of iterative sequences generated by the algorithms are also discussed.

• Journal of the Korean Mathematical Society
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• v.58 no.3
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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.

• Transactions of the Korean Society of Mechanical Engineers A
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• v.24 no.5 s.176
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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.

• Journal of the Institute of Electronics Engineers of Korea TC
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• v.42 no.7 s.337
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• pp.27-34
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• 2005

Iterative detection (ID) has proven to be a near-optimal solution for concatenated Finite State Machines (FSMs) with interleavers over an additive white Gaussian noise (AWGN) channel. When perfect channel state information (CSI) is not available at the receiver, an adaptive ID (AID) scheme is required to deal with the unknown, and possibly time-varying parameters. The basic building block for ID or AID is the soft-input soft-output (SISO) or adaptive SISO (A-SISO) module. In this paper, Reduced State SISO (RS-SISO) algorithms have been applied for complexity reduction of the A-SISO module. We show that serially concatenated CPM (SCCPM) with AID has turbo-like performance over fading ISI channels and also RS-A-SISO systems have large iteration gains. Various design options for RS-A-SISO algorithms are evaluated. Recently developed density evolution technique is used to analyze RS-A-SISO algorithms. We show that density evolution technique that is usually used for AWGN systems is also a good analysis tool for RS-A-SISO systems over frequency-selective fading channels.

• East Asian mathematical journal
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• v.17 no.1
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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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• v.13 no.1
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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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• v.5 no.2
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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.

• Journal of the Korean Mathematical Society
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• v.57 no.3
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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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• v.18 no.1
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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.

• Journal of the Korean Institute of Navigation
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• v.14 no.4
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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.