• Journal of the Korean Operations Research and Management Science Society
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• v.17 no.3
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• pp.171-180
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• 1992

This paper proposes a solution approach to linear problems with many constraints of variable upper bound (VUB) type. This type of constraints are commonly found in various scheduling type problems for which tighter bounds are essential to achieve an efficiency in enumeration. An analytical framework based on factorization is adopted to devise a solution approach to the problem and extend it for more generalized VUB problem (GVUB). This research shows why the VUB type constraints are amenable to the factorization and gives a unified approach to generalized upper bound(GUB) problems, VUB problems and GVUB problems. Implementation issues are also included.

• Journal of applied mathematics & informatics
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• v.16 no.1_2
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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.

• East Asian mathematical journal
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• v.19 no.1
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• pp.81-89
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• 2003

There are many algorithms for factoring integers. The trial division algorithm is one of the most efficient algorithms for factoring small integers(say less than 10,000,000,000). For a number n to be factored, the runtime of the trial division algorithm depends mainly on the size of a nontrivial factor of n. In this paper, we create a function named factors that can implement the trial division algorithm in ActionScript and using the factors function we construct an interactive Prime Factorization Movie and an interactive GCD Movie.

• Journal of the Chungcheong Mathematical Society
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• v.14 no.2
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• pp.55-66
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• 2001

A new stability analysis of QR factorizations using the two types of Householder reflections is presented. It shows that the use of the common type(the first) in QR factorizations with pivoting for size by row and column exchanges leas to rowwise more stability, although the second type has been used in Householder transformation for the better purpose. A row-oriented backward error bound for the second type Householder QR factorizations with column pivoting is drived.

• Communications of Mathematical Education
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• v.20 no.4 s.28
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• pp.587-594
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• 2006

In this paper we introduce a method of factorizing multi-variable polynomials using Viete's theorem and show some examples of factorizing multi-variable polynomials. We also discuss some aspects of this method.

• Communications of Mathematical Education
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• v.20 no.4 s.28
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• pp.595-602
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• 2006

In this paper we study an application of elementary symmetric polynomials related to transformation of homogeneous symmetric polynomials, factorization of polynomials, solving equation using elementary symmetric polynomials at the level of school mathematics.

• Journal of Korean Institute of Industrial Engineers
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• v.24 no.3
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• pp.407-416
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• 1998

For fast Cholesky factorization, it is most important to reduce the number of nonzero elements by ordering methods. Generally, the minimum deficiency ordering produces less nonzero elements, but it is very slow. We propose an efficient implementation method. The minimum deficiency ordering requires much computations related to adjacent nodes. But, we reduce those computations by using indistinguishable nodes, the clique storage structures, and the explicit storage structures to compute deficiencies.

• Communications of the Korean Mathematical Society
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• v.13 no.4
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• pp.801-810
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• 1998

Let A(z), W(z) and C(z) be power series with operator coefficients such that W(z) = A(z)C(z). Let D(A) and D(C) be the state spaces of unitary linear systems whose transfer functions are A(z) and C(z) respectively. Then there exists a Krein space D which is the state space of unitary linear system with transfer function W(z). And the element of D is of the form (f(z) ＋ A(z)h(z), k(z) ＋ C＊(z)g(z)) where (f(z),g(z)) is in D(A) and (h(z),k(z)) is in D(C).

• Journal of the Korea Institute of Information Security & Cryptology
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• v.1 no.1
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• pp.97-101
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• 1991

The polynomial factorization problem is important not only number theorly but chyptology with Discrete logarithm. We factorized polynolmials with integer coefficients by means of factori-zing polynomials on a finite field by Hensel's Lifting Lemma and finding factors of pol;ynomial with integer coeffcients.

• Journal of the Institute of Electronics and Information Engineers
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• v.54 no.1
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• pp.121-128
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• 2017

In this paper, we propose a dual-channel acoustic event detection (AED) method using nonnegative tensor factorization (NTF) and hidden Markov model (HMM) in order to improve detection accuracy of AED in multisource environments. The proposed method first detects multiple acoustic events by utilizing channel gains obtained from the NTF technique applied to dual-channel input signals. After that, an HMM-based likelihood ratio test is carried out to verify the detected events by using channel gains. The detection accuracy of the proposed method is measured by F-measures under 9 different multisource conditions. Then, it is also compared with those of conventional AED methods such as Gaussian mixture model and nonnegative matrix factorization. It is shown from the experiments that the proposed method outperforms the convectional methods under all the multisource conditions.