• 한국항행학회논문지
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• 제4권1호
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• pp.45-49
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• 2000

GPS에 의한 관측치는 시각오차, 전리층과 대류층 지연오차, 다중경로 오차와 같은 다양한 오차를 내포하고 있어서 GPS 관측치 위치계산시 일반적으로 최소자승해를 구하게 된다. GPS 관측치는 비선형 방정식을 만족하므로 최소자승해를 구하기 위해서는 비선형 Newton 알고리즘을 이용할 수도 있으나 대개 간편성과 효율성 때문에 선형화 알고리즘을 적용하게 된다. 본 연구에서는 비선형 Newton 알고리즘이나 선형화 알고리즘을 대체할 수 있는 부동점 알고리즘을 개발하여 그 유용성을 증명하였다. 비선형 Newton 알고리즘이나 선형화 알고리즘은 수렴속도가 빠른 장점을 가지고 있으나 초기값이 해와 근사하여야 한다는 단점이 있다. 반면 부동점 알고리즘은 수령속도는 다소 느리나 초기값이 대단히 부정확하여도 수렴가능한 장점이 있으므로 두 알고리즘을 적절히 혼용하는 것이 좋을 것이다.

• Journal of the Korean Society for Industrial and Applied Mathematics
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• 제2권2호
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• pp.41-47
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• 1998

We consider some numerical solution methods for equality-constrained quadratic problems in the context of structural analysis. Sparse orthogonal schemes for linear least squares problem are adapted to handle the solution step of the force method. We also examine these schemes with substructuring concepts.

• The Journal of the Acoustical Society of Korea
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• 제25권2E호
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• pp.43-48
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• 2006

Abstract-Using the recursive generalized eigendecomposition method, we develop a recursive form solution to the data least squares (DLS) problem, in which the error is assumed to lie in the data matrix only. Simulations demonstrate that DLS outperforms ordinary least square for certain types of deconvolution problems.

• Journal of applied mathematics & informatics
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• 제26권1_2호
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• pp.213-222
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• 2008

Iterative methods are often suitable for solving least squares problems min$||Ax-b||_2$, where A $\epsilon\;\mathbb{R}^{m{\times}n}$ is large and sparse. The well known LSQR algorithm is among the iterative methods for solving these problems. A good preconditioner is often needed to speedup the LSQR convergence. In this paper we present the numerical experiments of applying a well known preconditioner for the LSQR algorithm. The preconditioner is based on the $A^T$ A-orthogonalization process which furnishes an incomplete upper-lower factorization of the inverse of the normal matrix $A^T$ A. The main advantage of this preconditioner is that we apply only one of the factors as a right preconditioner for the LSQR algorithm applied to the least squares problem min$||Ax-b||_2$. The preconditioner needs only the sparse matrix-vector product operations and significantly reduces the solution time compared to the unpreconditioned iteration. Finally, some numerical experiments on test matrices from Harwell-Boeing collection are presented to show the robustness and efficiency of this preconditioner.

• Communications for Statistical Applications and Methods
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• 제17권2호
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• pp.141-151
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• 2010

Hybrid fuzzy regression analysis is used for integrating randomness and fuzziness into a regression model. Least squares support vector machine(LS-SVM) has been very successful in pattern recognition and function estimation problems for crisp data. This paper proposes a new method to evaluate hybrid fuzzy linear and nonlinear regression models with crisp inputs and fuzzy output using weighted fuzzy arithmetic(WFA) and LS-SVM. LS-SVM allows us to perform fuzzy nonlinear regression analysis by constructing a fuzzy linear regression function in a high dimensional feature space. The proposed method is not computationally expensive since its solution is obtained from a simple linear equation system. In particular, this method is a very attractive approach to modeling nonlinear data, and is nonparametric method in the sense that we do not have to assume the underlying model function for fuzzy nonlinear regression model with crisp inputs and fuzzy output. Experimental results are then presented which indicate the performance of this method.

• 제어로봇시스템학회논문지
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• 제17권10호
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• pp.1059-1066
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• 2011

This paper makes a close inquiry into ill-conditioning that may be occurred in wireless localization of the sensor nodes based on network signals in the wireless sensor network and provides the clue for solving the problem. In order to estimate the location of a node based on the range information calculated using the signal propagation time, LS (Least Squares) method is usually used. The LS method estimates the solution that makes the squared estimation error minimal. When a nonlinear function is used for the wireless localization, ILS (Iterative Least Squares) method is used. The ILS method process the LS method iteratively after linearizing the nonlinear function at the initial nominal point. This method, however, has a problem that the final solution may converge into a LM (Local Minimum) instead of a GM (Global Minimum) according to the deployment of the fixed nodes and the initial nominal point. The conditions that cause the problem are explained and an adaptive method is presented to solve it, in this paper. It can be expected that the stable location solution can be provided in implementation of the wireless localization methods based on the results of this paper.

• 한국전산구조공학회논문집
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• 제24권5호
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• pp.577-588
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• 2011

본 논문은 복합 불연속면을 갖는 포텐셜 문제의 해석을 위해 확장된 MLS(Moving Least Squares) 차분법을 제시한다. 계면경계를 따라 해(solution)와 수직방향, 접선방향 미분들이 모두 불연속 특이성을 나타내는 복합 불연속면을 묘사하기 위해 계단함수, 쐐기함수, 가위함수와 같은 불연속 특이함수를 추가하여 기존의 MLS 차분법을 개선했다. 계면경계조건은 기지의 조건으로서 지배방정식의 이산화과정에서 추가의 미지계수를 발생시키지 않는다. 포아송 방정식 형태의 지배미분 방정식을 풀기 위해 내부영역과 경계에 절점을 배치하고 차분식을 구성한다. 차분식을 조립한 계 방정식을 직접 풀기 때문에 계산효율성이 매우 우수하다. 수치예제는 제시된 해석기법의 우수성을 잘 보여주며, 균열전파, 이동경계, 상호작용 문제 등 다양한 불연속 문제로의 확장이 기대된다.

• 한국전산구조공학회논문집
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• 제20권4호
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• pp.501-507
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• 2007

본 연구의 전편에서는 이동최소제곱 유한차분법을 이용한 고체역학문제의 정식화 과정이 소개되었다. 후편에서는 수치예제를 통해 이동최소제곱 유한차분법의 정확성, 강건성, 효율성을 검증했다. 탄성론 문제의 해석을 통해 개발된 해석기법의 우수한 수렴률을 확인했다. 탄성균열문제에 적용하여 간편한 불연속면 모델링이 가능하고, 적응적 절점배치를 통해 특이 응력해를 정확하고 효율적으로 계산할 수 있음을 보였다. 국소화 밴드문제 해석결과를 통해 변위나 응력이 급격하게 변화하는 특수문제에 대한 정확성과 효율성을 확인했으며, 본 해석기법이 다양한 특수 공학적 문제로 확장될 수 있을 것으로 기대된다.

• International Journal of Control, Automation, and Systems
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• 제3권2호
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• pp.166-172
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• 2005

With the development of RAIM techniques for single failure, increasing interest has been shown in the multiple failure problem. As a result, numerous approaches have been used in attempts to tackle this problem. This paper considers the two failure problem with total least squares (TLS) technique, a solution that has rarely been addressed because TLS requires an immense number of computations. In this paper, the special form of the observation matrix H, (that is, one column is exactly known) is exploited so as to develop an algorithm in a sequential form, thereby reducing computational load. The algorithm permits the advantages of TLS without the excessive computational burden. The proposed algorithm is verified through a numerical simulation.

• 한국전산구조공학회:학술대회논문집
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• 한국전산구조공학회 2008년도 정기 학술대회
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• pp.2-7
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• 2008

A highly efficient moving least squares finite difference method (MLS FDM) for heat transfer analysis of composite material with interface. In the MLS FDM, governing differential equations are directly discretized at each node. No grid structure is required in the solution procedure. The discretization of governing equations are done by Taylor expansion based on moving least squares method. A wedge function is designed for the modeling of the derivative jump across the interface. Numerical examples showed that the numerical scheme shows very good computational efficiency together with high aocuracy so that the scheme for heat transfer problem with different heat conductivities was successfully verified.