• 한국정보처리학회논문지
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• 제2권1호
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• pp.55-65
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• 1995

다행관측행렬을 복원하는 기존의 알고리즘은 단일행의 복원방법인 Cholesky Factor Downdating(CFD) 을 이용하여 행렬 $Z^{T}$ 의 각 행을 순차적으로 복원하는 방법으로 필요한 실수연산의 횟수는 2/5 p $n^{2}$이다. 이에 비하여 본 논문에서 제안한 HCFD(Hybrid Cholesky Factor Downdating)기법은 p$\geq$n 인 크기의 다행관측행 렬 $Z^{T}$를 복원하는데 필요한 실수연산의 횟수가 p $n^{2}$＋6/5 $n^{3}$이다. HCFD 기법은 $Z^{T}$ 로부터 $Z^{T}$ = $Q_{z}$ RT/Z을 구하고, RT/Z에 대해 CFD 알고리즘을 적용함으로 필요한 시간복잡도를 크게 줄일 수 있다. 또한, HCFD 기법 과 기존의 CFD 기법을 Sun SPARC/2와 국산주전산기I에서 실험한 결과, HCFD 기법이 CFD기법에 비하여 성능이 우수함을 보여 주었으며, 특히 복원하려는 행이 많을 경우 에 HCFD기법이 CFD 기법에 비하여 성능이 크게 항상됨을 알 수 있었다.었다.

• Communications for Statistical Applications and Methods
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• 제21권2호
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• pp.169-181
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• 2014

Marginalized random effects models (MREM) are commonly used to analyze longitudinal categorical data when the population-averaged effects is of interest. In these models, random effects are used to explain both subject and time variations. The estimation of the random effects covariance matrix is not simple in MREM because of the high dimension and the positive definiteness. A relatively simple structure for the correlation is assumed such as a homogeneous AR(1) structure; however, it is too strong of an assumption. In consequence, the estimates of the fixed effects can be biased. To avoid this problem, we introduce one approach to explain a heterogenous random effects covariance matrix using a modified Cholesky decomposition. The approach results in parameters that can be easily modeled without concern that the resulting estimator will not be positive definite. The interpretation of the parameters is sensible. We analyze metabolic syndrome data from a Korean Genomic Epidemiology Study using this method.

• 경영과학
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• 제11권3호
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• pp.1-11
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• 1994

Recent advances in linear programming solution methodology have focused on interior point methods. This powerful new class of methods achieves significant reductions in computer time for large linear programs and solves problems significantly larger than previously possible. These methods can be examined from points of Fiacco and McCormick's barrier method, Lagrangian duality, Newton's method, and others. This study presents a primal-dual log barrier algorithm of interior point methods for linear programming. The primal-dual log barrier method is currently the most efficient and successful variant of interior point methods. This paper also addresses a Cholesky factorization method of symmetric positive definite matrices arising in interior point methods. A special structure of the matrices, called supernode, is exploited to use computational techniques such as direct addressing and loop-unrolling. Two dense matrix handling techniques are also presented to handle dense columns of the original matrix A. The two techniques may minimize storage requirement for factor matrix L and a smaller number of arithmetic operations in the matrix L computation.

• 한국경영과학회지
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• 제23권4호
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• pp.21-31
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• 1998

Ordering is used to reduce the amount of fill-ins in the Cholesky factor of an symmetric definite matrix. One of most efficient ordering methods is the minimum degree ordering method. In this paper. we propose the two techniques to improve the performance of the minimum degree ordering which are implemented using clique storage structure. One is node absorption which is a generalized version of clique absorption. The other technique is using the lower bounds of degree to suspend the degree updates of nodes. finally, we provide computational results on the problems on NETLIB. These results show that the proposed techniques reduce the number of degree updates and the computational time considerably.

• Geomechanics and Engineering
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• 제23권1호
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• pp.15-30
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• 2020

The probabilistic bearing capacity of a strip footing placed on the edge of a purely cohesive reinforced soil slope is computed by combining lower bound finite element limit analysis technique with random field method and Monte Carlo simulation technique. To simulate actual field condition, anisotropic random field model of undrained soil shear strength is generated by using the Cholesky-Decomposition method. With the inclusion of a single layer of reinforcement, dimensionless bearing capacity factor, N always increases in both deterministic and probabilistic analysis. As the coefficient of variation of the undrained soil shear strength increases, the mean N value in both unreinforced and reinforced slopes reduces for particular values of correlation length in horizontal and vertical directions. For smaller correlation lengths, the mean N value of unreinforced and reinforced slopes is always lower than the deterministic solutions. However, with the increment in the correlation lengths, this difference reduces and at a higher correlation length, both the deterministic and probabilistic mean values become almost equal. Providing reinforcement under footing subjected to eccentric load is found to be an efficient solution. However, both the deterministic and probabilistic bearing capacity for unreinforced and reinforced slopes reduces with the consideration of loading eccentricity.