• Journal of applied mathematics & informatics
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• v.29 no.5_6
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• pp.1179-1191
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• 2011

In this paper, we introduce a new iterative scheme for finding a common element of the set of fixed points of a finite family of strict pseudocontractions and the solution set of pseudomonotone and Lipschitz-type continuous equilibrium problems. The scheme is based on the idea of extragradient methods and fixed point iteration methods. We show that the iterative sequences generated by this algorithm converge strongly to the common element in a real Hilbert space.

• Journal of the Korean Mathematical Society
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• v.53 no.3
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• pp.691-707
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• 2016

In this paper, we first introduce two one-parameter relaxation (OPR) iterative methods for solving singular saddle point problems whose semi-convergence rate can be accelerated by using scaled preconditioners. Next we present formulas for finding their optimal parameters which yield the best semi-convergence rate. Lastly, numerical experiments are provided to examine the efficiency of the OPR methods with scaled preconditioners by comparing their performance with the parameterized Uzawa method with optimal parameters.

• Journal of applied mathematics & informatics
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• v.38 no.5_6
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• pp.489-506
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• 2020

The spatial fractional diffusion equation can be discretized by employing the implicit finite difference scheme using the shifted Grünwald formula. The discretized linear system is obtained, whose the coefficient matrix has a diagonal-plus-Toeplitz structure. In order to solve the diagonal-plus-Toeplitz linear system, on the basis of circulant and skew-circulant splitting (CSCS splitting), we construct a new and efficient iterative method, called DSCS iterative methods, which have two parameters. Than we prove the convergence of DSCS methods. As a focus, we derive the simple and effective values of two optimal parameters under some restrictions. Some numerical experiments are carried out to illustrate the validity and accuracy of the new methods.

• Journal of applied mathematics & informatics
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• v.28 no.3_4
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• pp.931-938
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• 2010

The disentangling map from the commutative algebra to the noncommutative algebra of operators is the essential operation of Feynman's operational calculus for noncommuting operators. Thus formulas which simplify this operation are meaningful to the subject. In a recent paper the procedure for "methods for iterative disentangling" has been established in the setting of Feynman's operational calculus for time independent operators $A_1$, $\cdots$, $A_n$ and associated probability measures${\mu}_1$, $\cdots$, ${\mu}_n$. The main purpose for this paper is to extend the procedure for methods for iterative disentangling to time dependent operators.

• Nonlinear Functional Analysis and Applications
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• v.27 no.2
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• pp.381-403
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• 2022

The main goal of this research is to solve variational inequalities involving quasimonotone operators in infinite-dimensional real Hilbert spaces numerically. The main advantage of these iterative schemes is the ease with which step size rules can be designed based on an operator explanation rather than the Lipschitz constant or another line search method. The proposed iterative schemes use a monotone and non-monotone step size strategy based on mapping (operator) knowledge as a replacement for the Lipschitz constant or another line search method. The strong convergences have been demonstrated to correspond well to the proposed methods and to settle certain control specification conditions. Finally, we propose some numerical experiments to assess the effectiveness and influence of iterative methods.

• Bulletin of the Korean Mathematical Society
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• v.41 no.1
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• pp.1-11
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• 2004

In this paper, we suggest and analyze some new classes of three step iterative algorithms for solving generalized quasivariational inclusions by using the properties of proximal maps. Our results include the Ishikawa, Mann iterations for solving variational inclusions(inequalities) as special cases. The results obtained in this paper represent an improvement and significant refinement of previously known results [3, 5-8, 10, 14-18].

• Journal of applied mathematics & informatics
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• v.34 no.5_6
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• pp.467-478
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• 2016

In this paper, we propose an Ishikawa-type extra-gradient iterative algorithm for finding a solution of split feasibility, fixed point problems and equilibrium problems of quasi-nonexpansive mappings. It is proven that under suitable conditions, the sequences generated by the proposed iterative algorithms converge weakly to a solution of the split feasibility, fixed point problems and equilibrium problems. An example is given to illustrate the main result of this paper.

• Korean Journal of Mathematics
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• v.21 no.3
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• pp.213-222
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• 2013

In this paper, we introduce and consider a new system of generalized variational inequalities involving five different operators. Using the sunny nonexpansive retraction technique we suggest and analyze some new explicit iterative methods for this system of variational inequalities. We also study the convergence analysis of the new iterative method under certain mild conditions. Our results can be viewed as a refinement and improvement of the previously known results for variational inequalities.

• Communications of the Korean Mathematical Society
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• v.26 no.1
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• pp.51-65
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• 2011

In this paper, a composite iterative process is introduced for a generalized equilibrium problem and a pair of nonexpansive mappings. It is proved that the sequence generated in the purposed composite iterative process converges strongly to a common element of the solution set of a generalized equilibrium problem and of the common xed point of a pair of nonexpansive mappings.

• The Transactions of the Korean Institute of Electrical Engineers
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• v.39 no.10
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• pp.1098-1107
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• 1990

Decentralized iterative learning control methods are presented for a class of large scale interconnected linear dynamic systems, in which iterative learning controller in each subsystem operates on its local subsystem exclusively with no exchange of information between subsystems. Suffcient conditions for convergence of the algorithms are given and numerical examples are illustrated to show the validity of the algorithms. In particular, the algorithms are useful for the systems having large uncertainty of inter-connected terms.