• Journal of applied mathematics & informatics
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• 제28권1_2호
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• pp.351-361
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• 2010

The solution of large sparse linear systems is one of the most important problems in large scale scientific computing. Among the many methods developed, the preconditioned Krylov subspace methods are considered the preferred methods. Selecting a suitable preconditioner with appropriate parameters for a specific sparse linear system presents a challenging task for many application scientists and engineers who have little knowledge of preconditioned iterative methods. The prediction of ILU type preconditioners was considered in [27] where support vector machine(SVM), as a data mining technique, is used to classify large sparse linear systems and predict best preconditioners. In this paper, we apply the data mining approach to the sparse approximate inverse(SAI) type preconditioners to find some parameters with which the preconditioned Krylov subspace method on the linear systems shows best performance.

• Journal of the Korean Society for Industrial and Applied Mathematics
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• 제20권3호
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• pp.225-242
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• 2016

The phase-type representation is strongly connected with the positive realization in positive system. We attempt to transform phase-type representation into sparse mono-cyclic positive representation with as low order as possible. Because equivalent positive representations of a given phase-type distribution are non-unique, it is important to find a simple sparse positive representation with lower order that leads to more effective use in applications. A Hypo-Feedback-Coxian Block (HFCB) representation is a good candidate for a simple sparse representation. Our objective is to find an HFCB representation with possibly lower order, including all the eigenvalues of the original generator. We introduce an efficient nonlinear optimization method for computing an HFCB representation from a given phase-type representation. We discuss numerical problems encountered when finding efficiently a stable solution of the nonlinear constrained optimization problem. Numerical simulations are performed to show the effectiveness of the proposed algorithm.

• 한국정보과학회:학술대회논문집
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• 한국정보과학회 1998년도 가을 학술발표논문집 Vol.25 No.2 (2)
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• pp.336-338
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• 1998

This paper presents a novel neural network structure to the blind deconvolution task where the input (source) to a system is not available and the source has any type of distribution including sparse distribution. We employ multiple sensors so that spatial information plays a important role. The resulting learning algorithm is linear so that it works for both sub-and super-Gaussian source. Moreover, we can successfully deconvolve the mixture of a sparse source, while most existing algorithms [5] have difficulties in this task. Computer simulations confirm the validity and high performance of the proposed algorithm.

• 정보관리학회지
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• 제40권2호
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• pp.59-80
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• 2023

기존의 연구자 유형 구분 모델은 대부분 연구성과 지표를 활용해왔다. 이 연구에서는 인용 영향력이 공동연구와 관련이 있다는 점을 감안하여 인용 데이터를 활용하지 않고 공동연구 지표만으로 연구자 유형을 분석하는 새로운 방법을 모색해보았다. 공동연구 패턴과 공동연구 범위를 기준으로 연구자를 Sparse & Wide (SW) 유형, Dense & Wide (DW) 유형, Dense & Narrow (DN) 유형, Sparse & Narrow (SN) 유형의 4가지로 구분하는 모델을 제안하였다. 제안된 모델을 양자계측 분야에 적용해본 결과, 구분된 연구자 유형별로 인용지표와 공저 네트워크 지표에 차이가 있음이 통계적으로 검증되었다. 이 연구에서 제시한 공동연구 특성에 따른 연구자 유형 구분 모델은 인용정보를 필요로 하지 않으므로 연구관리 정책과 연구지원서비스 측면에서 폭넓게 활용할 수 있을 것으로 기대된다.

• 대한토목학회논문집
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• 제11권4호
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• pp.143-150
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• 1991

이 논문은 대규모인 약 2,000점(미지수 약 4,000개)의 평면 측지망을 조정할 수 있는 프로그램을 개발하는데 목적이 있다. 데이터의 저장 및 관리에는 희박행렬(sparse matrix)의 기법이 사용되었으며, 관측방정식에는 RR(C)U (Row-Wise Representation Complete Unodered)방식, 정규방정식에는 RR(U)U(Row-Wise Representation Upper Unodered) 방식을 도입하고 해법에는 수정 Cholesky법을 적용하였다. PC 386에서 개발된 이 프로그램은 정밀 2차 기준점망인 테스트망에 적용되었으며, 2차원 배열을 사용한 Cholesky 분해법 및 직교분해법을 채용한 프로그램과의 상대적인 비교분석이 이루어졌다. 연구의 결과에서는 희박행렬의 기법이 기억용량의 면에서 뿐만 아니라 처리시간에 있어서도 극히 효과적인 기법임을 보여주고 있다.

• 정보처리학회논문지A
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• 제8A권3호
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• pp.227-234
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• 2001

In this paper we propose a block-type parallel preconditioner for solving large sparse nonsymmetric linear systems, which we expect to be scalable. It is Multi-Color Block SOR preconditioner, combined with direct sparse matrix solver. For the Laplacian matrix the SOR method is known to have a nondeteriorating rate of convergence when used with Multi-Color ordering. Since most of the time is spent on the diagonal inversion, which is done on each processor, we expect it to be a good scalable preconditioner. We compared it with four other preconditioners, which are ILU(0)-wavefront ordering, ILU(0)-Multi-Color ordering, SPAI(SParse Approximate Inverse), and SSOR preconditiner. Experiments were conducted for the Finite Difference discretizations of two problems with various meshsizes varying up to $1025{\times}1024$. CRAY-T3E with 128 nodes was used. MPI library was used for interprocess communications, The results show that Multi-Color Block SOR is scalabl and gives the best performances.

• 한국컴퓨터정보학회논문지
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• 제20권12호
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• pp.67-74
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• 2015

The heat conduction equation, a type of a Poisson equation which can be applied in various areas of engineering is calculating its value with the iteration method in general. The equation which had difference discretization of the heat conduction equation is the simultaneous equation, and each line has the characteristic of expressing in sparse matrix of the equivalent number of none-zero elements with neighboring grids. In this paper, we propose a data structure for sparse matrix that can calculate the value faster with less memory use calculate the heat conduction equation. To verify whether the proposed data structure efficiently calculates the value compared to the other sparse matrix representations, we apply the representative iteration method, CG (Conjugate Gradient), and presents experiment results of time consumed to get values, calculation time of each step and relevant time consumption ratio, and memory usage amount. The results of this experiment could be used to estimate main elements of calculating the value of the general heat conduction equation, such as time consumed, the memory usage amount.

• 대한수학회보
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• 제57권4호
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• pp.851-864
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• 2020

This paper gives a sparse domination for the iterated commutators of multilinear pseudo-differential operators with the symbol σ belonging to the Hörmander class, and establishes the quantitative bounds of the Bloom type estimates for such commutators. Moreover, the C_p estimates for the corresponding multilinear pseudo-differential operators are also obtained.

• Journal of applied mathematics & informatics
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• 제25권1_2호
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• pp.435-443
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• 2007

Computing the interior spectrum of large sparse generalized eigenvalue problems $Ax\;=\;{\lambda}Bx$, where A and b are large sparse and SPD(Symmetric Positive Definite), is often required in areas such as structural mechanics and quantum chemistry, to name a few. Recently, CG-type methods have been found useful and hence, very amenable to parallel computation for very large problems. Also, as in the case of linear systems proper choice of preconditioning is known to accelerate the rate of convergence. After the smallest eigenpair is found we use the orthogonal deflation technique to find the next m-1 eigenvalues, which is also suitable for parallelization. This offers advantages over Jacobi-Davidson methods with partial shifts, which requires re-computation of preconditioner matrx with new shifts. We consider as preconditioners Incomplete LU(ILU)(0) in two variants, ever-relaxation(SOR), and Point-symmetric SOR(SSOR). We set m to be 5. We conducted our experiments on matrices from discretizations of partial differential equations by finite difference method. The generated matrices has dimensions up to 4 million and total number of processors are 32. MPI(Message Passing Interface) library was used for interprocessor communications. Our results show that in general the Multi-Color ILU(0) gives the best performance.

• 응용통계연구
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• 제28권2호
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• pp.281-288
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• 2015

본 연구에서는 혼합모형의 추론을 위한 벌점-최대우도추정량의 빠른 계산절차를 제안하다. 제안된 절차는 벌점-최대우도추정량을 위한 추정방정식에서 헷시안 행렬을 화살촉형태를 지닌 희소행렬을 통하여 근사 시킴으로써 계산속도의 향상을 가져왔다. 두 가지 가상실험을 통하여 제안된 근사식을 사용함으로써 얻게되는 계산시간의 감소와 동시에 이를 위하여 지불하여야 하는 근사오차에 대하여 살펴보았다.