• Korean Management Science Review
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• v.19 no.2
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• pp.155-168
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• 2002

In this paper, some efficient implementation techniques for the multifrontal method, which can be used to compute the Cholesky factor of a symmetric positive definite matrix, are presented. In order to use the cache effect in the cache-based computer architecture, a hybrid method for factorizing a frontal matrix is considered. This hybrid method uses the column Cholesky method and the submatrix Cholesky method alternatively. Experiments show that the hybrid method speeds up the performance of the supernodal multifrontal method by 5%～10%, and it is superior to the Cholesky method in some problems with dense columns or large frontal matrices.

• Journal of the Korean Operations Research and Management Science Society
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• v.28 no.1
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• pp.51-61
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• 2003

In the normal equations approach in which the ordering and factorization phases are separated, the factorization in the augmented system approach is computed dynamically. This means that in the augmented system the numerical factorization should be performed to obtain the non-zero structure of Cholesky factor L. This causes much time to set up the non-zero structure of Cholesky factor L. So, we present a method which can separate the ordering and numerical factorization in the augmented system. Experimental results show that the proposed method reduces the time for obtaining the non-zero structure of Cholesky factor L.

• Communications for Statistical Applications and Methods
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• v.23 no.6
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• pp.587-592
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• 2016

It is a long-standing issue to correctly determine the number of long-run relationships among time series processes. We revisit nonparametric test for cointegration rank and propose bootstrap refinements. Consistent with model-free nature of the tests, we make use of Cholesky factor bootstrap methods, which require weak conditions for data generating processes. Simulation studies show that the original Breitung's test have difficulty in obtaining the correct size due to dependence in cointegrated errors. Our proposed bootstrapped tests considerably mitigate size distortions and represent a complementary approach to other bootstrap refinements, including sieve methods.

• The Journal of the Acoustical Society of Korea
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• v.12 no.2E
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• pp.47-62
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• 1993

SMI 방법은 수치적인 불안정성과 아울러 많은 계산량을 갖는다. 본 논문에서는 역 공분산 행렬의 Cholesky 분할을 이용하여 SMI 방법보다 효율적인 방법을 제안한다. 제안한 방법에서는 적응 빔 형상과 검출이 하나의 구조로 실현되며 이에 피룡한 역 공분산 행렬의 Cholesky factor는 secondary 입력으로부터 GS 프로세서를 이용하여 추정한다. 제안한 구조의 중요한 특징은 공분산 행렬과 Cholesky factor를 직접 구할 필요가 없다는 점이며, 또한 GS 프로세서의 장점을 이용한 systolic 구조를 사용함으로써 효율적인 계산을 수행할 수 있다. 모의 실험을 통하여 제안한 방법의 성능과 SMI 방법의 성능을 서로 비교하였다. 또한 nonhomogeneous 환경에서 동작하기 위한 방법이 제시되었으며, 아울러 계산량이 많은 GS 구조의 단점을 극복하기 위해 lattice-GS 구조를 이용하는 방법을 제안하였다.

• Journal of Korean Institute of Industrial Engineers
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• v.29 no.1
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• pp.78-89
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• 2003

Ordering is performed to reduce the amount of fill-ins of the Cholesky factor of a symmetric positive definite matrix. This paper proposes a new ordering algorithm that reduces the fill-ins of the Cholesky factor iteratively by elimination tree rotations and clique separators. Elimination tree rotations have been used mainly to reorder the rows of the permuted matrix for the efficiency of storage space management or parallel processing, etc. In the proposed algorithm, however, they are repeatedly performed to reduce the fill-ins of the Cholesky factor. In addition, we presents a simple method for finding a minimal node separator between arbitrary two nodes of a chordal graph. The proposed reordering procedure using clique separators enables us to obtain another order of rows of which the number of till-ins decreases strictly.

• Proceedings of the Korean Operations and Management Science Society Conference
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• 1996.10a
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• pp.289-292
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• 1996

In Cholesky factorization of the interior point method, dense columns of A matrix make dense Cholesky factor L regardless of sparsity of A matrix. We introduce a method to transform a primal problem to a dual problem in order to preserve the sparsity.

• KSII Transactions on Internet and Information Systems (TIIS)
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• v.13 no.2
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• pp.810-831
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• 2019

Recently, continuous dimensional emotion recognition from audiovisual clues has attracted increasing attention in both theory and in practice. The large amount of data involved in the recognition processing decreases the efficiency of most bimodal information fusion algorithms. A novel algorithm, namely the incomplete Cholesky decomposition based kernel cross factor analysis (ICDKCFA), is presented and employed for continuous dimensional audiovisual emotion recognition, in this paper. After the ICDKCFA feature transformation, two basic fusion strategies, namely feature-level fusion and decision-level fusion, are explored to combine the transformed visual and audio features for emotion recognition. Finally, extensive experiments are conducted to evaluate the ICDKCFA approach on the AVEC 2016 Multimodal Affect Recognition Sub-Challenge dataset. The experimental results show that the ICDKCFA method has a higher speed than the original kernel cross factor analysis with the comparable performance. Moreover, the ICDKCFA method achieves a better performance than other common information fusion methods, such as the Canonical correlation analysis, kernel canonical correlation analysis and cross-modal factor analysis based fusion methods.

• The Transactions of the Korea Information Processing Society
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• v.3 no.2
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• pp.359-368
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• 1996

This paper introduces PGD(Preprocessed Givens Downdating)and PHD(Preprocessed Hyperbolic Downdating) algorithms, wherein a multiple-row observation matrix $Z^T$ is factorized into a partial Cholesky factor Rz, such that $Z^T$ = $Q_zR_z, Q_zQ^T_z=I$, and then Rz is recursively downdated by using GD(Givens Downdating)and HD(Hyperbolic Dondating), respectively. Time complexities of PGD and PHD algorithms are $pn^2$ ＋ $5n^3/6$ 및 $pn^2$＋$n^3/3$ flops, respectively, if p$\geq$n, while those of the existing GD and HD are known to be $5pn^2/2$ and $2pn^2$ flops,, respectively. This concludes that the factorization of observation matrices, which we call preprocessing, would improve the overall performance of the downdating process. Benchmarks on the Sun SPARC/2 system also show that preprocessing would shorten the required downdating times compared to those of downdatings without preprocessing. Furthermore, benchmarks also show that PHD provides better performance than PGD.

• Management Science and Financial Engineering
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• v.8 no.1
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• pp.1-19
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• 2002

Ordering is used to reduce the amount of fill-ins in the Cholesky factor of a symmetric positive definite matrix. One of the most efficient ordering methods is the minimum degree ordering algorithm(MDO). In this paper, we provide a few techniques that improve the performance of MDO implemented with the clique storage scheme. First, the absorption of nodes in the cliques is developed which reduces the number of cliques and the amount of storage space required for MDO. Second, we present a modified minimum degree ordering algorithm of which the number of degree updates can be reduced by introducing the lower bounds of degrees. Third, using both the lower and upper bounds of degrees, we develop an approximate minimum degree ordering algorithm. Experimental results show that the proposed algorithm is competitive with the minimum degree ordering algorithm that uses quotient graphs from the points of the ordering time and the nonzeros in the Cholesky factor.

• KSCE Journal of Civil and Environmental Engineering Research
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• v.10 no.4
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• pp.95-101
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• 1990

Orthogonal decomposition technique, not using normal equation, but using observation equation directly, is accepted for adjusting the geodetic network in this paper. The results of study show that the technique is the numerically stable and powerful method in network adjustment by inner constraints or weighted position parameters. Also, it is suitable to middle sized-network and is applicable to Cholesky Factor in the normal equation system.