• Communications of the Korean Mathematical Society
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• v.11 no.4
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• pp.1175-1185
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• 1996

We study the computation of sparse null bases of equilibrium matrices in the context of structural optimization and incompressible fluid flow. In our approach we emphasize the parallel computatin and examine the applications. New block decomposition and node ordering schemes are suggested, and numerical examples are considered.

• Journal of the Korean Society for Precision Engineering
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• v.12 no.7
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• pp.99-106
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• 1995

Frequency response functions are of great use in dynamic analysis of structural systems. The present paper proposes an efficient method for computation of the frequency rewponse functions of linear structural dynamic models with a sparse, non-proportional damping matrix. An exact condensation procedure is proposed which enables the present method to condense the matrices without resulting in any errors. Also, an iterative scheme is proposed to be able to avoid matrix inversion in computing frequency response matrix. The proposed method is illustrated through a numerical example.

• The Korean Journal of Applied Statistics
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• v.28 no.2
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• pp.281-288
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• 2015

In this paper, we study an approximate procedure to evaluate a penalized maximum likelihood estimator (MLE) for a mixed effects model. The procedure approximates the Hessian matrix of the penalized MLE with a structured sparse matrix or an arrowhead type matrix to speed its computation. In this paper, we numerically investigate the gain in computation time as well as approximation error from the considered approximation procedure.

• The Transactions of the Korean Institute of Electrical Engineers C
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• v.49 no.1
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• pp.52-58
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• 2000

Signal propagation in nonlinear optical fiber is analyzed numerically by using SS-FEM (Split-Step Finite Element Method). By adopting cubic element function in FEM, soliton equation of which exact solution was well known, has been solved. Also, accuracy of numerical results and computing times are compared with those of Fourier method, and we have found that solution obtained from using FEM was very relatively accurate. Especially, to reduce CPU time in matrix computation in each step, the matrix imposed by the boundary condition is approximated as a sparse matrix. As a result, computation time was shortened even with the same or better accuracy when compared to those of the conventional FEM and Fourier method.

• Journal of Mechanical Science and Technology
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• v.15 no.8
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• pp.1090-1096
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• 2001

In this paper, new methods for efficiently solving linear acceleration equations of multibody dynamic simulation exploiting sparsity for real-time simulation are presented. The coefficient matrix of the equations tends to have a large number of zero entries according to the relative joint coordinate numbering. By adequate joint coordinate numbering, the matrix has minimum off-diagonal terms and a block pattern of non-zero entries and can be solved efficiently. The proposed methods, using sparse Cholesky method and recursive block mass matrix method, take advantages of both the special structure and the sparsity of the coefficient matrix to reduce computation time. The first method solves the η$\times$η sparse coefficient matrix for the accelerations, where η denotes the number of relative coordinates. In the second method, for vehicle dynamic simulation, simple manipulations bring the original problem of dimension η$\times$η to an equivalent problem of dimension 6$\times$6 to be solved for the accelerations of a vehicle chassis. For vehicle dynamic simulation, the proposed solution methods are proved to be more efficient than the classical approaches using reduced Lagrangian multiplier method. With the methods computation time for real-time vehicle dynamic simulation can be reduced up to 14 per cent compared to the classical approach.

• The Journal of Korean Institute of Communications and Information Sciences
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• v.17 no.7
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• pp.739-748
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• 1992

A CGM iterative systolic algorithm to solve large sparse linear systems of equations is presented. For implementation of the algorithm, a systolic array using the stripe structure is proposed. The matrix A is decomposed into a strictly lower triangular matrix, a diagonal matrix, and a strictly up-per triangular matrix, and the two formers and the tatter· are concurrently computed by different linear arrays. Hence, the execution time of this approach Is reduced to half of the execution time of the that a linear array is used. computation of the Irregularly distributed sparse matrix can be executed effectively by using the stripe structure.

• Journal of Information Processing Systems
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• v.16 no.6
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• pp.1359-1371
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• 2020

In transmitting and receiving such a large amount of data, reliable data communication is crucial for normal operation of a device and to prevent abnormal operations caused by errors. Therefore, in this paper, it is assumed that an error correction code (ECC) that can detect and correct errors by itself is used in an environment where massive data is sequentially received. Because an embedded system has limited resources, such as a low-performance processor or a small memory, it requires efficient operation of applications. In this paper, we propose using an accelerated ECC-decoding technique with a graphics processing unit (GPU) built into the embedded system when receiving a large amount of data. In the matrix-vector multiplication that forms the Hamming code used as a function of the ECC operation, the matrix is expressed in compressed sparse row (CSR) format, and a sparse matrix-vector product is used. The multiplication operation is performed in the kernel of the GPU, and we also accelerate the Hamming code computation so that the ECC operation can be performed in parallel. The proposed technique is implemented with CUDA on a GPU-embedded target board, NVIDIA Jetson TX2, and compared with execution time of the CPU.

• Journal of applied mathematics & informatics
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• v.28 no.3_4
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• pp.687-696
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• 2010

In this paper, an algorithm for computing the sparse approximate inverse factor of matrix $A^{T}\;A$, where A is an $m\;{\times}\;n$ matrix with $m\;{\geq}\;n$ and rank(A) = n, is proposed. The computation of the inverse factor are done without computing the matrix $A^{T}\;A$. The computed sparse approximate inverse factor is applied as a preconditioner for solving normal equations in conjunction with the CGNR algorithm. Some numerical experiments on test matrices are presented to show the efficiency of the method. A comparison with some available methods is also included.

• KSII Transactions on Internet and Information Systems (TIIS)
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• v.7 no.9
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• pp.2134-2153
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• 2013

A network-coding-based scheme is proposed to improve the energy efficiency of distributed storage systems in WSNs (Wireless Sensor Networks). We mainly focus on two problems: firstly, consideration is given to effective distributed storage technology; secondly, we address how to effectively repair the data in failed storage nodes. For the first problem, we propose a method to obtain a sparse generator matrix to construct network codes, and this sparse generator matrix is proven to be the sparsest. Benefiting from this matrix, the energy consumption required to implement distributed storage is reduced. For the second problem, we designed a network-coding-based iterative repair method, which adequately utilizes the idea of re-encoding at intermediate nodes from network coding theory. Benefiting from the re-encoding, the energy consumption required by data repair is significantly reduced. Moreover, we provide an explicit lower bound of field size required by this scheme, which implies that it can work over a small field and the required computation overhead is very low. The simulation result verifies that the proposed scheme not only reduces the total energy consumption required to implement distributed storage system in WSNs, but also balances energy consumption of the networks.

• The Journal of Korean Institute of Electromagnetic Engineering and Science
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• v.11 no.3
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• pp.337-344
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• 2000

The wavelet analysis technique is applied in the spectral domain to efficiently represent the multi-scale features of the impedance matrices. In this scheme, the 2-D quadtree decomposition (applying the wavelet transform to only the part of the matrix) method often used in image processing area is applied for a sparse moment matrix. CG(Conjugate-Gradient) method is also applied for saving memory and computation time of wavelet transformed moment matrix. Numerical examples show that for rectangular cylinder case the non-zero elements of the transformed moment matrix grows only as O($N^{1.6}$).