• 대한수학회지
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• 제55권1호
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• pp.83-99
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• 2018

We introduce the concept of multiplicatively closed subsets of a commutative ring R which split an R-module M and study factorization properties of elements of M with respect to such a set. Also we demonstrate how one can utilize this concept to investigate factorization properties of R and deduce some Nagata type theorems relating factorization properties of R to those of its localizations, when R is an integral domain.

• 대한수학회지
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• 제42권1호
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• pp.1-16
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• 2005

This paper presents a fast factorization algorithm for confluent Cauchy-like matrices. The algorithm consists of two parts. First. a confluent Cauchy-like matrix is transformed into a Cauchy-like matrix available to pivot without changing its structure. Second. a fast partial pivoting factorization algorithm for the Cauchy-like matrix is presented. A new displacement structure cannot possibly generate all entries of a transformed matrix, which is called by 'partially reconstructible'. This paper also discusses how the proposed factorization algorithm can be generally applied to partially reconstructive matrices.

• 한국수학사학회지
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• 제16권3호
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• pp.89-94
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• 2003

Though the concept of unique factorization was formulated in tile 19th century, Euclid already had considered the prime factorization of natural numbers, so called tile fundamental theorem of arithmetic. The unique factorization of algebraic integers was a crucial problem in solving elliptic equations and the Fermat Last Problem in tile 19th century On the other hand the unique factorization of the formal power series ring were a critical problem in the past century. Unique factorization is one of the idealistic condition in computation and prime elements and prime ideals are vital ingredients in thinking and solving problems.

• Journal of applied mathematics & informatics
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• 제8권3호
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• pp.705-720
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• 2001

We propose a variant of parallel block incomplete factorization preconditioners for a symmetric block-tridiagonal H-matrix. Theoretical properties of these block preconditioners are compared with those of block incomplete factoriztion preconditioners for the corresponding somparison matrix. Numerical results of the preconditioned CG(PCG) method using these block preconditioners are compared with those of PCG using other types of block incomplete factorization preconditioners. Lastly, parallel computations of the block incomplete factorization preconditioners are carried out on the Cray C90.

• 대한수학회보
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• 제43권2호
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• pp.419-424
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• 2006

In this paper we extend the study of ascend and descend of factorization properties (for atomic domains, domains satisfying ACCP, bounded factorization domains, half-factorial domains, pre-Schreier and semirigid domains) to the finite factorization domains and idf-domains for domain extension $A\;{\subseteq}\;B$.

• Journal of the Korean Statistical Society
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• 제19권1호
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• pp.45-53
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• 1990

Factorization models are a generalization of hierarchical loglinear models which apply equally to discrete and continuous distributions. In regular (strictly positive) cases the intersection of two factorization models is another factorization model whose representation is obtained by a simple algorithm. Failure of this result in an irregular case is related to a theorem of Basu on ancillary statistics.

• 한국정보통신학회논문지
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• 제10권7호
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• pp.1307-1311
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• 2006

본 연구에서는 행렬 분해 (Matrix Factorization)를 이용하여 음성 스펙트럼의 부분적 특정을 나타낼 수 있는 새로운 음성 파라마터를 제안한다. 제안된 파라미터는 행렬내의 모든 원소가 음수가 아니라는 조건에서 행렬분해 과정을 거치게 되고 고차원의 데이터가 효과적으로 축소되어 나타남을 알 수 있다. 차원 축소된 데이터는 입력 데이터의 부분적인 특성을 표현한다. 음성 특징 추출 과정에서 일반적으로 사용되는 멜 필터뱅크 (Mel-Filter Bank)의 출력 을 Non-Negative 행렬 분해(NMF:Non-Negative Matrix Factorization) 알고리즘의 입 력으로 사용하고, 알고리즘을 통해 차원 축소된 데이터를 음성인식기의 입력으로 사용하여 멜 주파수 캡스트럼 계수 (MFCC: Mel Frequency Cepstral Coefficient)의 인식결과와 비교해 보았다. 인식결과를 통하여 일반적으로 음성인식기의 성능평가를 위해 사용되는 MFCC에 비하여 제안된 특정 파라미터가 인식 성능이 뛰어남을 알 수 있었다.

• 한국경영과학회지
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• 제28권1호
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• pp.51-61
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• 2003

In the normal equations approach in which the ordering and factorization phases are separated, the factorization in the augmented system approach is computed dynamically. This means that in the augmented system the numerical factorization should be performed to obtain the non-zero structure of Cholesky factor L. This causes much time to set up the non-zero structure of Cholesky factor L. So, we present a method which can separate the ordering and numerical factorization in the augmented system. Experimental results show that the proposed method reduces the time for obtaining the non-zero structure of Cholesky factor L.

• 대한기계학회논문집A
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• 제27권2호
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• pp.276-284
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• 2003

The preconditioned conjugate gradient method is an efficient iterative solution scheme for large size finite element problems. As preconditioning method, we choose an incomplete Cholesky factorization which has efficiency and easiness in implementation in this paper. The incomplete Cholesky factorization mettled sometimes leads to breakdown of the computational procedure that means pivots in the matrix become minus during factorization. So, it is inevitable that a reduction process fur stabilizing and this process will guarantee robustness of the algorithm at the cost of a little computation. Recently incomplete factorization that enhances robustness through increasing diagonal dominancy instead of reduction process has been developed. This method has better efficiency for the problem that has rotational degree of freedom but is sensitive to parameters and the breakdown can be occurred occasionally. Therefore, this paper presents new method that guarantees robustness for this method. Numerical experiment shows that the present method guarantees robustness without further efficiency loss.

• 한국정보과학회논문지:컴퓨팅의 실제 및 레터
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• 제14권3호
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• pp.296-300
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• 2008

최근에 개발된 Nonnegative tensor factorization(NTF)는 비음수 행렬 분해(NMF)의 multiway(multilinear) 확장형이다. NTF는 CANDECOMP/PARAFAC 모델에 비음수 제약을 가한 모델이다. 본 논문에서는 Tucker 모델에 비음수 제약을 가한 nonnegative Tucker decomposition(NTD)라는 새로운 텐서 분해 모델을 제안한다. 제안된 NTD 모델을 least squares, I-divergence, $\alpha$-divergence를 이용한 여러 목적함수에 대하여 fitting하는 multiplicative update rule을 유도하였다.