• Bulletin of the Korean Mathematical Society
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• v.39 no.3
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• pp.495-509
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• 2002

We propose variants of the modified incomplete Cho1esky factorization preconditioner for a symmetric positive definite (SPD) matrix. Spectral properties of these preconditioners are discussed, and then numerical results of the preconditioned CG (PCG) method using these preconditioners are provided to see the effectiveness of the preconditioners.

• Journal of Korean Institute of Industrial Engineers
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• v.24 no.3
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• pp.407-416
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• 1998

For fast Cholesky factorization, it is most important to reduce the number of nonzero elements by ordering methods. Generally, the minimum deficiency ordering produces less nonzero elements, but it is very slow. We propose an efficient implementation method. The minimum deficiency ordering requires much computations related to adjacent nodes. But, we reduce those computations by using indistinguishable nodes, the clique storage structures, and the explicit storage structures to compute deficiencies.

• KSCE Journal of Civil and Environmental Engineering Research
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• v.11 no.4
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• pp.143-150
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• 1991

This paper presents an overview of a system of computer programs for the solution of a large geodetic network of about 2,000 stations. The system arranges the matrices in systematic sparse form which is applied to observation equations of RR(C)U (Row-wise Representation Complete Unordered) type and to normal equations of RR(U)U (Row-wise Representation Upper Unordered) type. The solution is done by a Modified Cholesky's algorithm in view of large networks. The implementation program are tested in PC-386 by korean new secondary networks, the results show that the sparse techniques are highly useful to geodetic networks in core-storage management and processing time.

• 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.

• Proceedings of the Korean Institute of Information and Commucation Sciences Conference
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• 2014.10a
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• pp.295-298
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• 2014

In this paper, an efficient design of HEVC Adaptive Loop Filter(ALF) for filter coefficients estimation is proposed. The ALF performs Cholesky decomposition of $10{\times}10$ matrix iteratively to estimate filter coefficients. The Cholesky decomposition of the ALF consists of root and division operation which is difficult to implement in a hardware design because it needs to many computation rate and processing time due to floating-point unit operation of large values of the Maximum 30bit in a LCU($64{\times}64$). The proposed hardware architecture is implemented by designing a root operation based on Cholesky decomposition by using multiplexer, subtracter and comparator. In addition, The proposed hardware architecture of efficient and low computation rate is implemented by designing a pipeline architecture using characteristic operation steps of Cholesky decomposition. An implemented hardware is designed using Xilinx ISE 14.3 Vertex-6 XC6VCX240T FPGA device and can support a frame rate of 40 4K Ultra HD($4096{\times}2160$) frames per second at maximum operation frequency 150MHz.

• Proceedings of the Korean Operations and Management Science Society Conference
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• 1991.10a
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• pp.24-24
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• 1991

• 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.

• Proceedings of the KIEE Conference
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• 1996.07a
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• pp.68-70
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• 1996

In this paper, an efficient parallel computation method for solving large sparse systems of linear algebraic equations by using Cholesky's method in the finite element method is studied. The methods of minimizing the number of fill-ins in the factorization process of factorization are investigated for minimizing the amount of memory and computation time. The parallel programming is implemented under the PVM(Parallel Virtual Machine) environment. The method of load-distribution is studied for minimizing the computation time and the communication time.

• 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.