• Journal of applied mathematics & informatics
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• v.25 no.1_2
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• pp.415-424
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• 2007

The generalized inverses have many important applications in the aspects of theoretic research and numerical computations and therefore they were studied by many authors. In this paper we get some necessary and sufficient conditions of the forward order law for {1}-inverse of multiple matrices products $A\;=\;A_1A_2{\cdots}A_n$ by using the maximal rank of generalized Schur complement.

• Proceedings of the Korean Operations and Management Science Society Conference
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• 2003.11a
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• pp.191-194
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• 2003

As internet commerce grows, many company has begun to use a CF (Collaborative Filtering) as a Recommender System. To achieve an accuracy of CF, we need to obtain sufficient account of voting scores from customers. Moreover, those scores may not be consistent. To overcome this problem, we propose a new recommendation scheme using binary user-item matrix, which represents whether a user purchases a product instead of using the voting scores. Through the experiment regarding this new scheme, a better accuracy is demonstrated.

• Journal of applied mathematics & informatics
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• v.12 no.1_2
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• pp.165-182
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• 2003

Toeplitz matrix method and the product Nystrom method are described for mixed Fredholm-Volterra singular integral equation of the second kind with Carleman Kernel and logarithmic kernel. The results are compared with the exact solution of the integral equation. The error of each method is calculated.

• Bulletin of the Korean Mathematical Society
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• v.43 no.2
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• pp.343-352
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• 2006

A real matrix A is called a sign-central matrix if for, every matrix $\tilde{A}$ with the same sign pattern as A, the convex hull of columns of $\tilde{A}$ contains the zero vector. A sign-central matrix A is called a tight sign-central matrix if the Hadamard (entrywise) product of any two columns of A contains a negative component. A real vector x = $(x_1,{\ldots},x_n)^T$ is called stable if $\|x_1\|{\leq}\|x_2\|{\leq}{\cdots}{\leq}\|x_n\|$. A tight sign-central matrix is called a $tight^*$ sign-central matrix if each of its columns is stable. In this paper, for a matrix B, we characterize those matrices C such that [B, C] is tight ($tight^*$) sign-central. We also construct the matrix C with smallest number of columns among all matrices C such that [B, C] is $tight^*$ sign-central.

• Proceedings of the IEEK Conference
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• 1998.10a
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• pp.807-810
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• 1998

This paper propose the method to produce GRM(Generalized Reed-Muller)expansion. The general method to obtain GRM expansion coefficient for p valued n variable is derivation of single variable transform matrix and expand it n times using Kronecker product. In this case the size of matrix increases depending on the augmentation of variables. In this paper we propose the simple algorithm to produce GRM coefficient using a single variable transform matrix.

• Journal of applied mathematics & informatics
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• v.34 no.1_2
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• pp.95-106
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• 2016

In this paper, according to the classical LSQR algorithm forsolving least squares (LS) problem, an iterative method is proposed for finding the minimum-norm pure imaginary solution of the quaternionic least squares (QLS) problem. By means of real representation of quaternion matrix, the QLS's correspongding vector algorithm is rewrited back to the matrix-form algorthm without Kronecker product and long vectors. Finally, numerical examples are reported that show the favorable numerical properties of the method.

• Journal of the Korean Mathematical Society
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• v.55 no.2
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• pp.327-342
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• 2018

In this paper, a homotopy continuation method for obtaining the unique Hermitian positive definite solution of the nonlinear matrix equation $X-{\sum_{i=1}^{m}}A^{\ast}_iX^{-p_i}A_i=I$ with $p_i$ > 1 is proposed, which does not depend on a good initial approximation to the solution of matrix equation.

• Journal of the Korean Institute of Telematics and Electronics
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• v.24 no.1
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• pp.173-176
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• 1987

This paper presents a simple factorization of the Hadamard matrix which is used to develop a fast algorithm for the Hadamard transform. This matrix decomposition is of the kronecker products of identity matrices and successively lower order Hadamard matrices. This following shows how the Kronecker product can be mathematically defined and efficiently implemented using a factorization matrix methods.

• Journal of the Korean Statistical Society
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• v.25 no.3
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• pp.393-406
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• 1996

We obtain the general moment of non-central Wishart distribu-tion, using the J-th moment of a matrix quadratic form and the 2J-th moment of the matrix normal distribution. As an example, the second moment and kurtosis of non-central Wishart distribution are also investigated.

• Analytical Science and Technology
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• v.20 no.2
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• pp.176-182
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• 2007

The present study relates to a matrix-typed, sustained-releasing agent comprising agrochemical effective ingredients being capable of recognizing a content of moisture, and a preparation method thereof. The curdlan solution added to acid was formed matrix which has unique network structure. The matrix treated by heat lost water solubility. The network structure of matrix was opened in the aquatic condition but closed again in dry condition. Therefore, in the sustained-releasing formulation system, an agrochemical effective ingredient was released from the formulation only in the aquatic condition. Use of the composition according to the product can control a manifesting time of effects of agrochemicals and can provide agrochemicals with reduced harmful damages.