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

• 대한수학회지
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• 제56권6호
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• pp.1503-1514
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• 2019

A rank 1 matrix has a factorization as $uv^t$ for vectors u and v of some orders. The arctic rank of a rank 1 matrix is the half number of nonzero entries in u and v. A matrix of rank k can be expressed as the sum of k rank 1 matrices, a rank 1 decomposition. The arctic rank of a matrix A of rank k is the minimum of the sums of arctic ranks of the rank 1 matrices over all rank 1 decomposition of A. In this paper we obtain characterizations of the linear operators that strongly preserve the symmetric arctic ranks of symmetric matrices over nonnegative reals.

• 한국정보통신학회논문지
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• 제10권4호
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• pp.645-651
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• 2006

본 논문은 컴퓨터 시스템의 성능평가와 분석을 대칭구조의 멀티프로세서를 실행할 수 있는 시뮬레이터를 사용하여 살펴보았으며 또한 시스템 분석을 하는데 있어서 멀티프로세서를 위한 멀티프로그램 벤치마크의 집합체인 SPLASH-2를 이행하여 대칭구조의 운영체제 IRIX5.3 탑재한 멀티프로세서의 행위범위의 연구를 수행하기 위하여 멀티프로세서의 시스템 분석을 실시 하였다. 또한 대칭구조의 멀티프로세서의 구조와 평가방법을 보다 유효하게 하기 위해서 멀티프로세서의 확장성을 functionality-based 소프트웨어인 SimOS를 가지고 증명하였으며 본 논문을 통하여 멀티프로그램 벤치마크인 RADIX 정렬 알고리즘이나 Cholesky 인수분해 알고리즘을 이용하여 로칼 인스트럭션과 로칼 데이터 사이에서의 멀티프로세서의 Cache miss의 수 와 Stall 시간을 동시에 검사하였다.

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

• Journal of the Korean Society for Industrial and Applied Mathematics
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• 제3권1호
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• pp.99-106
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• 1999

An accelerated optimization technique combined with a stepwise deflation procedure is presented for the efficient evaluation of a few of the smallest eigenvalues and their corresponding eigenvectors of the generalized eigenproblems. The optimization is performed on the Rayleigh quotient of the deflated matrices by the aid of a preconditioned conjugate gradient scheme with the incomplete Cholesky factorization.

• 경영과학
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• 제19권2호
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• pp.155-168
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• 2002

In this paper, some efficient implementation techniques for the multifrontal method, which can be used to compute the Cholesky factor of a symmetric positive definite matrix, are presented. In order to use the cache effect in the cache-based computer architecture, a hybrid method for factorizing a frontal matrix is considered. This hybrid method uses the column Cholesky method and the submatrix Cholesky method alternatively. Experiments show that the hybrid method speeds up the performance of the supernodal multifrontal method by 5%～10%, and it is superior to the Cholesky method in some problems with dense columns or large frontal matrices.

• Journal of applied mathematics & informatics
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• 제23권1_2호
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• pp.25-42
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• 2007

A direct solver for the Legendre tau approximation for the two-dimensional Poisson problem is proposed. Using the factorization of symmetric eigenvalue problem, the algorithm overcomes the weak points of the Schur decomposition and the conventional diagonalization techniques for the Legendre tau approximation. The convergence of the method is proved and numerical results are presented.

• 경영과학
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• 제11권3호
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• pp.1-11
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• 1994

Recent advances in linear programming solution methodology have focused on interior point methods. This powerful new class of methods achieves significant reductions in computer time for large linear programs and solves problems significantly larger than previously possible. These methods can be examined from points of Fiacco and McCormick's barrier method, Lagrangian duality, Newton's method, and others. This study presents a primal-dual log barrier algorithm of interior point methods for linear programming. The primal-dual log barrier method is currently the most efficient and successful variant of interior point methods. This paper also addresses a Cholesky factorization method of symmetric positive definite matrices arising in interior point methods. A special structure of the matrices, called supernode, is exploited to use computational techniques such as direct addressing and loop-unrolling. Two dense matrix handling techniques are also presented to handle dense columns of the original matrix A. The two techniques may minimize storage requirement for factor matrix L and a smaller number of arithmetic operations in the matrix L computation.

• KSII Transactions on Internet and Information Systems (TIIS)
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• 제17권1호
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• pp.74-96
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• 2023

At present, the smart grid has become one of the indispensable infrastructures in people's lives. As a commonly used communication method, wireless communication is gradually, being widely used in smart grid systems due to its convenient deployment and wide range of serious challenges to security. For the insecurity of the schemes based on large integer factorization and discrete logarithm problem in the quantum environment, an identity-based key management scheme for smart grid over lattice is proposed. To assure the communication security, through constructing intra-cluster and inter-cluster multi-hop routing secure mechanism. The time parameter and identity information are introduced in the relying phase. Through using the symmetric cryptography algorithm to encrypt improve communication efficiency. Through output the authentication information with probability, the protocol makes the private key of the certification body no relation with the distribution of authentication information. Theoretic studies and figures show that the efficiency of keys can be authenticated, so the number of attacks, including masquerade, reply and message manipulation attacks can be resisted. The new scheme can not only increase the security, but also decrease the communication energy consumption.