• Journal of applied mathematics & informatics
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• 제27권1_2호
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• pp.1-12
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• 2009

Iterative algorithms are proposed for the least-squares symmetric solution of AXB = E with a submatrix constraint. We characterize the linear mappings from their independent element space to the constrained solution sets, study their properties and use these properties to propose two matrix iterative algorithms that can find the minimum and quasi-minimum norm solution based on the classical LSQR algorithm for solving the unconstrained LS problem. Numerical results are provided that show the efficiency of the proposed methods.

• Kyungpook Mathematical Journal
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• 제62권1호
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• pp.89-106
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• 2022

We are concerned with finding a common solution to an equilibrium problem associated with a bifunction, and a constrained convex minimization problem. We propose an iterative fixed point algorithm and prove that the algorithm generates a sequence strongly convergent to a common solution. The common solution is identified as the unique solution of a certain variational inequality.

• International Journal of Aeronautical and Space Sciences
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• 제9권2호
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• pp.79-86
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• 2008

High performance direct-iterative hybrid linear solver for large scale finite element problem is developed. Direct solution method is robust but difficult to parallelize, whereas iterative solution method is opposite for direct method. Therefore, combining two solution methods is desired to get both high performance parallel efficiency and numerical robustness for large scale structural analysis problems. Hybrid method mentioned in this paper is based on FETI-DP (Finite Element Tearing and Interconnecting-Dual Primal method) which has good parallel scalability and efficiency. It is suitable for fourth and second order finite element elliptic problems including structural analysis problems. We are using the hybrid concept of theses two solution method categories, combining the multifrontal solver into FETI-DP based iterative solver. Hybrid solver is implemented for our general structural analysis code, IPSAP.

• Journal of applied mathematics & informatics
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• 제26권5_6호
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• pp.1233-1245
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• 2008

In this paper, an iterative method is proposed to solve the least-squares problem of matrix equation AXB+CYD=E over unknown matrix pair [X, Y]. By this iterative method, for any initial matrix pair [$X_1,\;Y_1$], a solution pair or the least-norm least-squares solution pair of which can be obtained within finite iterative steps in the absence of roundoff errors. In addition, we also consider the optimal approximation problem for the given matrix pair [$X_0,\;Y_0$] in Frobenius norm. Given numerical examples show that the algorithm is efficient.

• ETRI Journal
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• 제37권3호
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• pp.533-540
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• 2015

In wireless localization, several linear closed-form solution (LCS) methods have been investigated as a direct result of the drawbacks that plague the existing iterative methods, such as the local minimum problem and heavy computational burden. Among the known LCS methods, both the direct solution method and the difference of squared range measurements method are considered in this paper. These LCS methods do not have any of the aforementioned problems that occur in the existing iterative methods. However, each LCS method does have its own individual error property. In this paper, a hybrid LCS method is presented to reduce these errors. The hybrid LCS method integrates the two aforementioned LCS methods by using two check points that give important information on the probability of occurrence of each LCS's individual error. The results of several Monte Carlo simulations show that the proposed method has a good performance. The solutions provided by the proposed method are accurate and reliable. The solutions do not have serious errors such as those that occur in the conventional standalone LCS and iterative methods.

• 한국컴퓨터정보학회논문지
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• 제7권1호
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• pp.48-53
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• 2002

본 논문에서는 Rural Postman Problem(RPP) 해법을 위한 Iterative Local Search(ILS) 알고리즘을 제안한다. ILS 알고리즘은 초기해를 여러 번 생성하여 탐색 시작점을 달리하는 방법으로, 초기해의 설정 방법에 따라 알고리즘의 성능이 크게 좌우되는 Local Search(LS) 알고리즘의 단점을 보완할 수 있다. 본 논문에서는 LS 알고리즘과 ILS 알고리즘을 18개의 RPP 문제에 적용하고 그 성능을 분석한다. 실험 결과에서는 ILS 알고리즘이 각각 다른 탐색 시작점에서 해 공간을 탐색함으로서 LS에 비해 좋은 해를 찾을 수 있음을 알 수 있었다.

• 대한수학회지
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• 제53권1호
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• pp.89-114
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• 2016

In this paper, we introduce and study an explicit hybrid relaxed extragradient iterative method to approximate a common solution to generalized mixed equilibrium problem and fixed point problem for a nonexpansive semigroup in Hilbert space. Further, we prove that the sequence generated by the proposed iterative scheme converges strongly to the common solution to generalized mixed equilibrium problem and fixed point problem for a nonexpansive semigroup. This common solution is the unique solution of a variational inequality problem and is the optimality condition for a minimization problem. The results presented in this paper are the supplement, improvement and generalization of the previously known results in this area.

• 대한기계학회논문집
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• 제19권7호
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• pp.1651-1656
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• 1995

The adhesively bonded tubular single lap joint shows large nonlinear behavior in the loaddisplacement relation, because structural adhesives for the joint are usually rubber toughened, which endows adhesives with nonlinear shear properties. since the majority of load transfer of the adhesively bonded tubular single lap joint is accomplished by the nonlinear behavior of the adhesive, its torque transmission capability should be calculated incorporating nonlinear shear properties. However, both the analytic and numerical analyses become complicated if the nonlinear shear properties of the adhesive are included during the calculation of torque transmission capabilities. In this paper, in order to obtain the torque transmission capabilities easily, an iterative solution which includes the nonlinear shear properties of the adhesive was derived using the analytic solution with the linear shear properties of the adhesive. Since the iterative solution can be obtained very fast due to its simplicity, it has been found that it can be used in the design of the adhesively bonded tubular single lap joint.

• Journal of applied mathematics & informatics
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• 제34권5_6호
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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.

• East Asian mathematical journal
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• 제17권2호
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• pp.265-273
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• 2001

In this paper, we prove that under certain conditions the Ishikawa iterative method with errors converges strongly to the unique solution of the nonlinear strongly accretive operator equation Tx=f. Related results deal with the solution of the equation x+Tx=f. Our results extend and improve the corresponding results of Liu, Childume, Childume-Osilike, Tan-Xu, Deng, Deng-Ding and others.