• 인터넷정보학회논문지
• /
• 제12권3호
• /
• pp.131-137
• /
• 2011

GPGPU는 원래 그래픽 계산을 위한 프로세서인 GPU를 일반 계산에 활용하여 저전력으로 고성능의 효율을 보이는 신개념의 계산 장치이다. 본 논문에서는 GPGPU에서 계산을 하기 위한 병렬 LU 분해법의 알고리즘을 제안하였다. Nvidia GPGPU에서 프로그램을 실행하기 위한 CUDA 계산 환경에서는 계산하고자 하는 데이터 도메인을 블록으로 나누고 각 블록을 쓰레드들이 동시에 계산을 하는데, 이 때 블록들의 계산 순서는 무작위로 진행이 되기 때문에 블록간의 데이터 의존성을 가지는 LU 분해 프로그램에서는 결과가 정확하지 않게 된다. 본 논문에서는 병렬 LU 분해법에서 블록간의 계산 순서를 인위적으로 정하는 구현 방식을 제안하며 아울러 LU 분해법의 부분 피벗팅을 계산하기 위한 병렬 reduction 알고리즘도 제안한다. 또한 구현된 병렬프로그램의 성능 분석을 통하여 GPGPU의 멀티 쓰레드 기반으로 고성능으로 계산할 수 있는 병렬프로그램의 효율성을 보인다.

• Kyungpook Mathematical Journal
• /
• 제52권4호
• /
• pp.359-373
• /
• 2012

The block LU factorization is used to solve the coupled Stokes equations arisen from an optimal control problem subject to Stokes equations. The convergence of the spectral element solution is proved. Some numerical evidences are provided for the model coupled Stokes equations. Moreover, as an application, this algorithm is performed for an optimal control problem.

• East Asian mathematical journal
• /
• 제39권5호
• /
• pp.523-528
• /
• 2023

Let S_n = [S(i, j)]_1≤i,j≤n and S^*_n = [S(i + j, j)]_1≤i,j≤n where S(i, j) is the Stirling number of the second kind. Choi and Jo [On the determinants of the square-type Stirling matrix and Bell matrix, Int. J. Math. Math. Sci. 2021] obtained the diagonal entries of matrix U in the LU-factorization of S^*_n for calculating the determinant of S^*_n, where L = S_n. In this paper, we compute the all entries of U in the LU-factorization of matrix S^*_n. This implies the identities related to Stirling numbers of both kinds.

• 대한수학회지
• /
• 제36권1호
• /
• pp.209-227
• /
• 1999

We propose new parallel block ILU (Incomplete LU) factorization preconditioners for a nonsymmetric block-tridiagonal M-matrix. Theoretial properties of these block preconditioners are studied to see the convergence rate of the preconditioned iterative methods, Lastly, numerical results of the right preconditioned GMRES and BiCGSTAB methods using the block ILU preconditioners are compared with those of these two iterative methods using a standard ILU preconditioner to see the effectiveness of the block ILU preconditioners.

• Journal of applied mathematics & informatics
• /
• 제16권1_2호
• /
• pp.19-35
• /
• 2004

We develop in this paper some preconditioners for sparse non-symmetric M-matrices, which combine a recursive two-level block I LU factorization with multigrid method, we compare these preconditioners on matrices arising from discretized convection-diffusion equations using up-wind finite difference schemes and multigrid orderings, some comparison theorems and experiment results are demonstrated.

• Journal of applied mathematics & informatics
• /
• 제8권2호
• /
• pp.305-326
• /
• 2001

We introduce a class of multilevel recursive incomplete LU preconditioning techniques (RILUM) for solving general sparse matrices. This techniques is based on a recursive two by two block incomplete LU factorization on the coefficient martix. The coarse level system is constructed as an (approximate) Schur complement. A dynamic preconditioner is obtained by solving the Schur complement matrix approximately. The novelty of the proposed techniques is to solve the Schur complement matrix by a preconditioned Krylov subspace method. Such a reduction process is repeated to yield a multilevel recursive preconditioner.

• 대한전기학회:학술대회논문집
• /
• 대한전기학회 2000년도 하계학술대회 논문집 A
• /
• pp.274-275
• /
• 2000

This paper introduces new ordering algorithms using the graph of data structure and forward/backward substitution of LU decomposition using recursive function. The performance of the algorithm is compared with Tinney's algorithm using 14 bus systems. Test results show that the new fill-in element of Jacobian matrix using the proposed ordering algorithm is same as that of Tinner scheme 3 and the forward/backward substitution can reduce the computation time

• Journal of applied mathematics & informatics
• /
• 제22권1_2호
• /
• pp.307-316
• /
• 2006

Incomplete LU factorization preconditioning techniques often have difficulty on indefinite sparse matrices. We present hybrid reordering strategies to deal with such matrices, which include new diagonal reorderings that are in conjunction with a symmetric nondecreasing degree algorithm. We first use the diagonal reorderings to efficiently search for entries of single element rows and columns and/or the maximum absolute value to be placed on the diagonal for computing a nonsymmetric permutation. To augment the effectiveness of the diagonal reorderings, a nondecreasing degree algorithm is applied to reduce the amount of fill-in during the ILU factorization. With the reordered matrices, we achieve a noticeable improvement in enhancing the stability of incomplete LU factorizations. Consequently, we reduce the convergence cost of the preconditioned Krylov subspace methods on solving the reordered indefinite matrices.

• 한국전산유체공학회:학술대회논문집
• /
• 한국전산유체공학회 2002년도 추계 학술대회논문집
• /
• pp.95-102
• /
• 2002

Studies of the numerical characteristics of implicit upwind schemes, such as upwind ADI, Line Gauss-Seidel(LGS) and Point Gauss-Seidel(LU) algorithms, for preconditioned Navier-Stokes equations ate performed. All the algorithms are expressed in approximate factorization form and Von Neumann stability analysis and convergence studies are made. Preconditioning is applied for efficient convergence at low Mach numbers and low Reynolds numbers. For high aspect ratio computations, the ADI and LGS algorithms show efficient and uniform convergence up to moderate aspect ratio if we adopt viscous preconditioning based on min- CFL/max- VNN time-step definition. The LU algorithm, on the other hand, shows serious deterioration in convergence rate as the grid aspect ratio increases. Computations for practical applications also verify these results.

• 정보보호학회논문지
• /
• 제15권2호
• /
• pp.65-72
• /
• 2005

최근 Zhou, Cao 그리고 Lu는 강한 위조 불가능을 만족하는 RSA와 소인수 분해 문제 기반의 세 가지 대리서명기법을 제안하면서 각각의 대리서명 기법들이 랜덤 오라클 모델하에서 증명가능한 안전성을 제공한다는 주장을 하였다. 본 논문에서는 이 기법들이 원 서명자로부터 위임받지 않은 사용자도 유효한 대리서명을 생성할 수 있게 한다는 점을 보임으로써 대리서명이 만족해야 하는 기본적인 안전성을 만족하지 않는다는 것을 보인다.