• International Journal of Automotive Technology
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• 제2권3호
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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.

• 인터넷정보학회논문지
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• 제14권6호
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• pp.41-47
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• 2013

GP-GPU는 그래픽 처리를 위한 GPU의 다중쓰레드를 일반 수치 계산에 활용하여 초고속으로 계산하는 장치이다. GP-GPU에서는 CPU의 캐시메모리와는 달리 다중쓰레드가 공유하는 공유메모리의 형태로 캐시메모리를 제공하며, 공유메모리는 사용자 프로그램에서 직접 제어할 수 있다. 본 연구에서는 GP-GPU의 캐시메모리를 사용하여 계산 성능을 향상시키기 위한 블록 구조의 병렬 LU 분해 프로그램을 구현하였다. Nvidia CUDA C로 구현된 병렬 블록 LU 분해 프로그램은 동일한 GP-GPU 상에서 일반 LU 분해 프로그램에 비교하여 7~8배 이상의 속도 개선을 보였다.

• 대한기계학회논문집A
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• 제21권8호
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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.

• 한국철도학회논문집
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• 제5권3호
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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.

• 한국산업융합학회 논문집
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• 제4권1호
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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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• 제어로봇시스템학회 1997년도 한국자동제어학술회의논문집; 한국전력공사 서울연수원; 17-18 Oct. 1997
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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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• 제12권4호
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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.

• 한국통신학회논문지
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• 제16권6호
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• pp.556-565
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• 1991

A가 nxn 삼중대각행렬인 선형방정식 Ax=b를 WZ분해 알고리즘을 이용하여 해석하고 이 알고리즘을 CAM Systolic Array 로 구현했다. 그리고 이 어레이를 평가하기위하여 LU분해 알고리즘을 제시하고 이를 W, D, Z분해 알고리즘과 비교 고찰한 결과 LU분해 알고리즘 보다 WZ분해 알고리즘이 1/4정도 가까운 시간으로 실행시간이 단축될 수 있었다. CAM Systolic Array에서 실행되는 각 단계를 1 time stpe으로 가정하면 2n+1 times이 필요하고 CAM의 데이타 워드는 메트릭스 원소의 값과 행번호, 연산의 형태 및 상태에 관한 정보를 포함하고 pipeline식으로 각 프로세서를 systolic processing하므로서 중앙제어가 필요없고, data brodcasting도 피할 수 있다.

• 전기전자학회논문지
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• 제2권2호
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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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• 제17권1_2_3호
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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.