• Journal of the Korean Society for Industrial and Applied Mathematics
• /
• 제22권2호
• /
• pp.101-113
• /
• 2018

The dual singular function method(DSFM) is a numerical algorithm to get optimal solution including corner singularities for Poisson and Helmholtz equations. In this paper, we apply DSFM to solve heat equation which is a time dependent problem. Since the DSFM for heat equation is based on DSFM for Helmholtz equation, it also need to use Sherman-Morrison formula. This formula requires linear solver n + 1 times for elliptic problems on a domain including n reentrant corners. However, the DSFM for heat equation needs to pay only linear solver once per each time iteration to standard numerical method and perform optimal numerical accuracy for corner singularity problems. Because the Sherman-Morrison formula is rather complicated to apply computation, we introduce a simplified formula by reanalyzing the Sherman-Morrison method.

• 한국통신학회논문지
• /
• 제39A권9호
• /
• pp.566-568
• /
• 2014

본 논문에서는 대규모 MIMO 시스템을 위한 MMSE 기반 반복 연판정 간섭 제거 기법을 제안한다. 제안 기법은 기존 기법에서의 연산량 감소를 위해 Sherman-Morrison-Woodbury 식을 사용하여 매 Iteration 마다 단 한 번의 역행렬 계산으로 모든 송신 심볼의 MMSE 검출 벡터를 계산한다. 모의실험을 통해 제안 기법이 대규모 MIMO 시스템에서 기존 기법과 거의 동일한 BER을 달성함을 확인하였다.

• 대한수학회보
• /
• 제55권2호
• /
• pp.431-448
• /
• 2018

This paper is concerned with the positive definite solutions of the nonlinear matrix equation $X-A^*{\bar{X}}^{-1}A=Q$, where A, Q are given complex matrices with Q positive definite. We show that such a matrix equation always has a unique positive definite solution and if A is nonsingular, it also has a unique negative definite solution. Moreover, based on Sherman-Morrison-Woodbury formula, we derive elegant relationships between solutions of $X-A^*{\bar{X}}^{-1}A=I$ and the well-studied standard nonlinear matrix equation $Y+B^*Y^{-1}B=Q$, where B, Q are uniquely determined by A. Then several effective numerical algorithms for the unique positive definite solution of $X-A^*{\bar{X}}^{-1}A=Q$ with linear or quadratic convergence rate such as inverse-free fixed-point iteration, structure-preserving doubling algorithm, Newton algorithm are proposed. Numerical examples are presented to illustrate the effectiveness of all the theoretical results and the behavior of the considered algorithms.

• Journal of Electrical Engineering and Technology
• /
• 제7권4호
• /
• pp.493-500
• /
• 2012

In this paper the performance of meta-heuristics algorithms such as GA (Genetic Algorithm), DE (Differential Evolution), PSO (Particle Swarm Optimization) and SA (Simulated Annealing) for the problem of TTC enhancement using FACTS devices are compared. In addition to that in the assessment procedure of TTC two novel techniques are proposed. First the optimization algorithm which is used for TTC enhancement is simultaneously used for assessment of TTC. Second the power flow is done using Broyden - Shamanski method with Sherman - Morrison formula (BSS). The proposed approach is tested on WSCC 9 bus, IEEE 118 bus test systems and the results are compared with the conventional Repeated Power Flow (RPF) using Newton Raphson (NR) method which indicates that the proposed method provides better TTC enhancement and computational efficacy than the conventional procedure.

• Structural Engineering and Mechanics
• /
• 제52권1호
• /
• pp.149-172
• /
• 2014

Four algorithms for damage detection of trusses are presented in this paper. These approaches can detect damage by using both complete and incomplete measurements. The suggested methods are based on the minimization of the difference between the measured and analytical static responses of structures. A non-linear constrained optimization problem is established to estimate the severity and location of damage. To reach the responses, the successive quadratic method is used. Based on the objective function, the stiffness matrix of the truss should be estimated and inverted in the optimization procedure. The differences of the proposed techniques are rooted in the strategy utilized for inverting the stiffness matrix of the damaged structure. Additionally, for separating the probable damaged members, a new formulation is proposed. This scheme is employed prior to the outset of the optimization process. Furthermore, a new tactic is presented to select the appropriate load pattern. To investigate the robustness and efficiency of the authors' method, several numerical tests are performed. Moreover, Monte Carlo simulation is carried out to assess the effect of noisy measurements on the estimated parameters.

• 한국항공우주학회지
• /
• 제47권7호
• /
• pp.499-507
• /
• 2019

고정익 항공기의 수학적 모델이 잘 알려져 있음에도 불구하고, 넓은 비행 영역에서 모델링 오차를 고려하여 설계 제어 성능을 달성하기 위한 다양한 연구가 있다. 본 논문은 레벤버그-마쿼트 알고리듬을 적용한 모델-참조 적응 제어 법칙과, 이를 이용한 고정익 무인항공기의 피치 자세 제어에 대한 연구를 소개한다. 또한 모델-참조 적응 제어의 기준 모델을 모델의 동특성에 기인하여 결정함으로써 성능지표를 제시한다. 설계한 적응 법칙의 성능은 시뮬레이션과 비행실험을 통해 검증했다.