• Journal of applied mathematics & informatics
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• v.33 no.5_6
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• pp.627-633
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• 2015

In this paper, we generalize the concept of the energy of Seidel matrix S(G) which denoted by S^α(G) and obtain some results related to this matrix. Also, we obtain an upper and lower bound for S^α(G) related to all of graphs with |detS(G)| ≥ (n - 1); n ≥ 3.

• ETRI Journal
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• v.36 no.1
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• pp.167-170
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• 2014

In this letter, we propose an unsupervised framework for speech noise reduction based on the recent development of low-rank and sparse matrix decomposition. The proposed framework directly separates the speech signal from noisy speech by decomposing the noisy speech spectrogram into three submatrices: the noise structure matrix, the clean speech structure matrix, and the residual noise matrix. Evaluations on the Noisex-92 dataset show that the proposed method achieves a signal-to-distortion ratio approximately 2.48 dB and 3.23 dB higher than that of the robust principal component analysis method and the non-negative matrix factorization method, respectively, when the input SNR is -5 dB.

• Honam Mathematical Journal
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• v.28 no.3
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• pp.333-342
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• 2006

We denote by Q(A) the set of all matrices with the same sign pattern as A. A matrix A is an SN-matrix provided there exists a set S of sign patterns such that the set of sign patterns of vectors in the null-space of A is S, for each A ${\in}$ Q(A). We have a characterization of an SN-matrix related with L-matrix and we analyze the structure of an SN-matrix.

• KSII Transactions on Internet and Information Systems (TIIS)
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• v.13 no.11
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• pp.5616-5630
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• 2019

Fully homomorphic encryption allows a third-party to perform arbitrary computation over encrypted data and is especially suitable for secure outsourced computation. This paper investigates secure outsourced computation of multiple matrix multiplication based on fully homomorphic encryption. Our work significantly improves the latest Mishra et al.'s work. We improve Mishra et al.'s matrix encoding method by introducing a column-order matrix encoding method which requires smaller parameter. This enables us to develop a binary multiplication method for multiple matrix multiplication, which multiplies pairwise two adjacent matrices in the tree structure instead of Mishra et al.'s sequential matrix multiplication from left to right. The binary multiplication method results in a logarithmic-depth circuit, thus is much more efficient than the sequential matrix multiplication method with linear-depth circuit. Experimental results show that for the product of ten 32×32 (64×64) square matrices our method takes only several thousand seconds while Mishra et al.'s method will take about tens of thousands of years which is astonishingly impractical. In addition, we further generalize our result from square matrix to non-square matrix. Experimental results show that the binary multiplication method and the classical dynamic programming method have a similar performance for ten non-square matrices multiplication.

• Journal of the Korean Mathematical Society
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• v.50 no.4
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• pp.755-770
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• 2013

One of the interesting nonlinear matrix equations is the quadratic matrix equation defined by $$Q(X)=AX^2+BX+C=0$$, where X is a $n{\times}n$ unknown real matrix, and A, B and C are $n{\times}n$ given matrices with real elements. Another one is the matrix polynomial $$P(X)=A_0X^m+A_1X^{m-1}+{\cdots}+A_m=0,\;X,\;A_i{\in}\mathbb{R}^{n{\times}n}$$. Newton's method is used to find the symmetric and bisymmetric solvents of the nonlinear matrix equations Q(X) and P(X). The method does not depend on the singularity of the Fr$\acute{e}$chet derivative. Finally, we give some numerical examples.

• Journal of the Korean Statistical Society
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• v.22 no.2
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• pp.249-258
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• 1993

It is well known that design matrix X for any factorial design can be represented by a product $X = TX_o$ where T is replication matrix and $X_o$ is the corresponding balanced design matrix. Since $X_o$ consists of regular arrangement of 0's and 1's, we can easily find the spectral decomposition of $X_o',X_o$. Also using this we propose an efficient algorithm for computing the orthogonal projection matrix for a balanced factorial design.

• Journal of applied mathematics & informatics
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• v.33 no.3_4
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• pp.247-260
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• 2015

The special form of Schur complement is extended to have a Schur's formula to obtains the explicit formula of determinant, inverse, and eigenvector formula of the doubly Leslie matrix which is the generalized forms of the Leslie matrix. It is also a generalized form of the doubly companion matrix, and the companion matrix, respectively. The doubly Leslie matrix is a nonderogatory matrix.

• Journal of applied mathematics & informatics
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• v.27 no.5_6
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• pp.1061-1071
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• 2009

For real generalized reflexive matrices R, S, i.e., $R^T$ = R, $R^2$ = I, $S^T$ = S, $S^2$ = I, we say that real matrix X is (R,S)-symmetric, if RXS = X. In this paper, an iterative algorithm is proposed to solve the least-squares problem of matrix equation AXB = C with (R,S)-symmetric X. Furthermore, the optimal approximation solution to given matrix $X_0$ is also derived by this iterative algorithm. Finally, given numerical example and its convergent curve show that this method is feasible and efficient.

• Journal of the Korean Vacuum Society
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• v.1 no.1
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• pp.115-120
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• 1992

SIMS is an indispensable surface analysis instrument in trace element depth profiling because of high detection sensitivity and excellent depth resolution, however, it requires a standard sample to do quantitative analysis due to matrix effect depending on the species of impurities and sample matricies and on the sputtering rates. Among the SNMS technology developed to supply the deficiency, we researched into CsX+ SNMS which improved the result quantitatively without any extra epuipments. So basic SNMS functions were confirmed through matrix element composition rate analysis using Siq layer etc., and adaptability to trace element concentration alaysis was tried. For that purpose we compared SIMS depth profile data for Boron which presented strong matrix effect on account of Fluorin existence after BF2 ion implantation on silicon substrate with SNMS data. Also detection limit and dynamic range were investigated. After these experements we concluded that CsX+ SNMS reduced matrix effect and we could apply it to profile impurity elements.

• Communications of the Korean Mathematical Society
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• v.12 no.2
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• pp.269-273
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• 1997

We show that each element in the semigroup $S_n$ of all $n \times n$ non-singular stochastic totally positive matrices is generated by the infinitesimal elements of $S_n$, which form a cone consisting of all $n \times n$ Jacobi intensity matrices.