• International Journal of Automotive Technology
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• v.2 no.3
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• pp.117-122
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• 2001

For a dynamic analysis of a constrained multibody system, it is necessary to have a routine for satisfying kinematic constraints. LU decomposition scheme, which is used to divide coordinates into dependent and independent coordinates, is efficient but has great difficulty near the singular configuration. Other method such as the projection matrix, which is more stable near a singular configuration, takes longer simulation time due to the large amount of calculation for decomposition. In this paper, the row space and the null space of the Jacobian matrix are proposed by using the pseudo-inverse method and the projection matrix. The equations of the motion of a system are replaced with independent acceleration components using the null space of the Jacobian matrix. Also a new hybrid method is proposed, combining the LU decomposition and the projection matrix. The proposed hybrid method has following advantages. (1) The simulation efficiency is preserved by the LU method during the simulation. (2) The accuracy of the solution is also achieved by the projection method near the singular configuration.

• Journal of Internet Computing and Services
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• v.14 no.6
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• pp.41-47
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• 2013

GP-GPUs are general purposed GPUs for numerical computation based on multiple threads which are originally for graphic processing. GP-GPUs provide cache memory in a form of shared memory which user programs can access directly, unlikely typical cache memory. In this research, we implemented the parallel block LU decomposition program to utilize cache memory in GP-GPUs. The parallel blocked LU decomposition program designed with Nvidia CUDA C run 7~8 times faster than nun-blocked LU decomposition program in the same GP-GPU computation environment.

• Transactions of the Korean Society of Mechanical Engineers A
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• v.21 no.8
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• pp.1311-1321
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• 1997

In multibody dynamics, differential and algebraic equations which can satisfy both equation of motion and kinematic constraint equation should be solved. To solve these equations, coordinate partitioning method and constraint stabilization method are commonly used. In the coordinate partitioning method, the coordinates are divided into independent and dependent and coordinates. The most typical coordinate partitioning method are LU decomposition, QR decomposition, and SVD (singular value decomposition). The objective of this research is to find an efficient coordinate partitioning method in the dynamic analysis of flexible multibody systems. Comparing two coordinate partitioning methods, i.e. LU and QR decomposition in the flexible multibody systems, a new hybrid coordinate partitioning method is suggested for the flexible multibody analysis.

• Journal of the Korean Society for Railway
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• v.5 no.3
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• pp.174-180
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• 2002

In multibody dynamics, DAE(Differential Algebraic Equations) that combine differential equations of motion and kinematic constraint equations should be solved. To solve these equations, either coordinate partitioning method or constraint stabilization method is commonly used. The most typical coordinate partitioning methods are LU decomposition, QR decomposition, and SVD(singular value decomposition). The objective of this research is to suggest a hybrid coordinate partitioning method in the dynamic analysis of multibody systems containing singular configurations. Two coordinate partitioning methods, i.e. LU decomposition and QR decomposition for constrained multibody systems, are combined for a new hybrid coordinate partitioning method. The proposed hybrid method reduces the simulation time while keeping accuracy of the solution.

• Journal of the Korean Society of Industry Convergence
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• v.4 no.1
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• pp.87-94
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• 2001

In multibody dynamics, differential and algebraic equations which can satisfy both equation of motion and kinematic constraint equation should be solved. To solve this equation, coordinate partitioning method and constraint stabilization method are commonly used. The coordinate partitioning method divides the coordinate into independent and dependent coordinates. The most typical coordinate partitioning method arc LU decomposition, QR decomposition, projection method and SVD(sigular value decomposition).The objective of this research is to find a efficient coordinate partitioning method in flexible multibody systems and a hybrid decomposition algorithm which employs both LU and projection methods is proposed. The accuracy of the solution algorithm is checked with a slider-crank mechanism.

• 제어로봇시스템학회:학술대회논문집
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• 1997.10a
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• pp.1762-1765
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• 1997

Some ill-conditioned processes are very sensitive to small element-wise uncertainties arising in classical element-by-element model identifications. For such processes, accurate identification of simgular values and right singular vectors are more important than theose of the elements themselves. Singular values and right singular vectors can be found by iteraive identification methods which implement the input and output transformations iteratively. Methods based on SVD decomposition, QR decomposition and LU decomposition are proposed and compared with the Kuong and Mac Gregor's method. Convergence proofs are given. These SVD and QR mehtods use normal matrices for the transformations which cannot be calculated analytically in general and so they are hoard to apply to dynamic processes, whereas the LU method used simple analyitc transformations and can be directly applied to dynamic processes.

• Journal of Information Processing Systems
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• v.12 no.4
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• pp.765-778
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• 2016

In watermarking schemes, the discrete wavelet transform (DWT) is broadly used because its frequency component separation is very useful. Moreover, LU decomposition has little influence on the visual quality of the watermark. Hence, in this paper, a novel blind watermark algorithm is presented based on LU transform and DWT for the copyright protection of digital images. In this algorithm, the color host image is first performed with DWT. Then, the horizontal and vertical diagonal high frequency components are extracted from the wavelet domain, and the sub-images are divided into $4{\times}4$ non-overlapping image blocks. Next, each sub-block is performed with LU decomposition. Finally, the color image watermark is transformed by Arnold permutation, and then it is inserted into the upper triangular matrix. The experimental results imply that this algorithm has good features of invisibility and it is robust against different attacks to a certain degree, such as contrast adjustment, JPEG compression, salt and pepper noise, cropping, and Gaussian noise.

• The Journal of Korean Institute of Communications and Information Sciences
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• v.16 no.6
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• pp.556-565
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• 1991

Using the WDZ decomposition algorithm, a parallel algorithm is presented for solving the linear system Ax=b which has an nxn nonsingular tridiagonal matrix. For implementing this algorithm a CAM systolic arrary is proposed, and each processing element of this array has its own CAM to store the nonzero elements of the tridiagonal matrix. In order to evaluate this array the algorithm presented is compared to theis compared to the LU decomposition algorithm. It is found that the execution time of the algorithm presented is reduced to about 1/4 than that of the LU decomposition algorithm. If each computation process step can be dome in one time unit, the system of eqations is solved in a systolic fashion without central control is obtained in 2n+1 time steps.

• Journal of IKEEE
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• v.2 no.2 s.3
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• pp.247-254
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• 1998

This paper presents a performance study of two LU decomposition algorithms on two massively parallel SIMD machines: the 16K processor MasPar MP-1 and the 4K processor MasPar MP-2. The paper presents experimental results and an analysis of the algorithms to explain the results. While the blocked and the nonblocked algorithms for LU decomposition have been studied individually by others, we compare the two algorithms and identify the tradeoffs between them. Our analysis of the blocked algorithm shows how the block size affects the interprocessor communication cost and the memory read/write overhead. The analysis in this paper is useful to determine an optimum block size for the blocked algorithm.

• Journal of applied mathematics & informatics
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• v.17 no.1_2_3
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• pp.585-590
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• 2005

An efficient procedure for finding the inverse of a nonsingular matrix is developed by solving directly for the UL decomposition of the inverse based on the entries of the original nonsingular matrix.