• Journal of applied mathematics & informatics
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• 제27권5_6호
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• pp.1061-1071
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• 2009

For real generalized reflexive matrices R, S, i.e., $R^T$ = R, $R^2$ = I, $S^T$ = S, $S^2$ = I, we say that real matrix X is (R,S)-symmetric, if RXS = X. In this paper, an iterative algorithm is proposed to solve the least-squares problem of matrix equation AXB = C with (R,S)-symmetric X. Furthermore, the optimal approximation solution to given matrix $X_0$ is also derived by this iterative algorithm. Finally, given numerical example and its convergent curve show that this method is feasible and efficient.

• Journal of Electrical Engineering and Technology
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• 제9권1호
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• pp.80-89
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• 2014

A stochastic optimal power flow (S-OPF) model considering uncertainties of load and wind power is developed based on chance constrained programming (CCP). The difficulties in solving the model are the nonlinearity and probabilistic constraints. In this paper, a limit relaxation approach and an iterative learning control (ILC) method are implemented to solve the S-OPF model indirectly. The limit relaxation approach narrows the solution space by introducing regulatory factors, according to the relationship between the constraint equations and the optimization variables. The regulatory factors are designed by ILC method to ensure the optimality of final solution under a predefined confidence level. The optimization algorithm for S-OPF is completed based on the combination of limit relaxation and ILC and tested on the IEEE 14-bus system.

• Korean Journal of Mathematics
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• 제18권3호
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• pp.299-309
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• 2010

In this paper, we study the first order nonlinear neutral difference equation: $${\Delta}(x(n)+px(n-{\tau}))+f(n,x(n-c),x(n-d))=r(n),\;n{\geq}n_0$$. Using the Banach fixed point theorem, we prove the existence of bounded positive solutions of the equation, suggest Mann iterative schemes of bounded positive solutions, and discuss the error estimates between bounded positive solutions and sequences generated by Mann iterative schemes.

• 호남수학학술지
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• 제26권4호
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• pp.391-399
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• 2004

In this paper, we develop an iterative algorithm for solving a class of nonlinear mixed implicit variational inequalities in Hilbert spaces. The resolvent operator technique is used to establish the equivalence between variational inequalities and fixed point problems. This equivalence is used to study the existence of a solution of nonlinear mixed implicit variational inequalities and to suggest an iterative algorithm for solving variational inequalities. In our results, we do not assume that the mapping is strongly monotone.

• 대한수학회보
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• 제44권4호
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• pp.861-870
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• 2007

In this paper, under suitable conditions, we show that the new class of iterative process with errors introduced by Li et al converges strongly to the unique solution of the equation involving strongly accretive operators in real Banach spaces. Furthermore, we prove that it is equivalent to the classical Ishikawa iterative sequence with errors.

• 대한수학회논문집
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• 제15권2호
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• pp.309-323
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• 2000

The purposes of this paper are to revise the definitions of Ishikawa and Mann type iterative processes with errors, to study the unique solution of the m-accretive operator equation x+Tx=f and the convergence problem of Ishikawa and Mann type iterative processes with errors for m-accretive mappings without the Lipschitz condition. The results presented in this paper improve, extend, and unify the corresponding results in [4, 7, 8, 12, 16] in more general setting.

• International Journal of Naval Architecture and Ocean Engineering
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• 제9권4호
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• pp.390-403
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• 2017

Smoothed Particle Hydrodynamics (SPH) method has a good adaptability for the simulation of free surface flow problems. There are two forms of SPH. One is weak compressible SPH and the other one is incompressible SPH (ISPH). Compared with the former one, ISPH method performs better in many cases. ISPH based on Rankine source solution can perform better than traditional ISPH, as it can use larger stepping length by avoiding the second order derivative in pressure Poisson equation. However, ISPH_R method needs to solve the sparse linear matrix for pressure Poisson equation, which is one of the most expensive parts during one time stepping calculation. Iterative methods are normally used for solving Poisson equation with large particle numbers. However, there are many iterative methods available and the question for using which one is still open. In this paper, three iterative methods, CGS, Bi-CGstab and GMRES are compared, which are suitable and typical for large unsymmetrical sparse matrix solutions. According to the numerical tests on different cases, still water test, dam breaking, violent tank sloshing, solitary wave slamming, the GMRES method is more efficient than CGS and Bi-CGstab for ISPH method.

• KSII Transactions on Internet and Information Systems (TIIS)
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• 제8권2호
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• pp.424-442
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• 2014

Most recent research on iterative solutions for interference alignment (IA) presents solutions assuming channel reciprocity based on the suppression of interference from undesired sources by using an appropriate decoding matrix also known as a receiver combining matrix for multiple input multiple output (MIMO) interference channel networks and reciprocal networks. In this paper, we present an alternative solution for IA by designing precoding and decoding matrices based on the concept of signal leakage (the measure of signal power that leaks to unintended users) on each transmit side. We propose an iterative algorithm for an IA solution based on maximization of the signal-to-leakage-and-noise ratio (SLNR) of the transmitted signal from each transmitter. In order to make an algorithm removing the requirement of channel reciprocity, we deploy maximization of the signal-to-interference-and-noise ratio (SINR) in the design of the decoding matrices. We show through simulation that minimizing the leakage in each transmission can help achieve enhanced performance in terms of aggregate sum capacity in the system.

• 한국전산구조공학회논문집
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• 제13권3호
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• pp.305-319
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• 2000

본 논문에서는 대변형 비선형 변형체의 마찰 접촉 문제의 해법을 제시하였다. 접촉 가능 점에서 접촉조건을 접촉오차 벡터를 이용하여 표시하였으며, 이러한 접촉오차 벡터를 0으로 단조 감소시키기 위하여 반복계산법을 사용하였다. 각 반복계산은 2개의 단계로 구성되어 있다 : 첫 단계에서는 이미 구해진 해의 기하학적 모양에서 얻어지는 접촉오차 벡터를 이용하여 접촉력을 수정하고, 두 번째 단계에서는 첫 단계의 접촉력을 이용하여 평형방정식을 풀어서 변위 및 접촉오차를 계산하는 것이다. 본 반복계산법에 의하여 정확한 해를 얻을 수 있음을 설명하였으며, 강소성 막 및 비선형 탄성보를 사용하여 예제계산을 수행하였다.

• Journal of applied mathematics & informatics
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• 제25권1_2호
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• pp.329-337
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• 2007

In the paper, we obtain the existence of positive solutions and establish a corresponding iterative scheme for BVPs $$\{^{\;(\phi_p(u'))'\;+\;q(t)f(t,u)=0,\;0\;<\;t\;<\;1,}_{\;u(0)\;-\;B(u'({\eta}))\;=\;0,\;u'(1)\;=\;0}$$ and $$\{^{\;(\phi_p(u'))'\;+\;q(t)f(t,u)=0,\;0\;<\;t\;<\;1,}_{\;u'(0)\;=\;0,\;u(1)+B(u'(\eta))\;=\;0.}$$. The main tool is the monotone iterative technique. Here, the coefficient q(t) may be singular at t = 0, 1.