• Journal of the Korean Mathematical Society
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• v.36 no.1
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• pp.209-227
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• 1999

We propose new parallel block ILU (Incomplete LU) factorization preconditioners for a nonsymmetric block-tridiagonal M-matrix. Theoretial properties of these block preconditioners are studied to see the convergence rate of the preconditioned iterative methods, Lastly, numerical results of the right preconditioned GMRES and BiCGSTAB methods using the block ILU preconditioners are compared with those of these two iterative methods using a standard ILU preconditioner to see the effectiveness of the block ILU preconditioners.

• Journal of the Korean Institute of Telematics and Electronics S
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• v.34S no.1
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• pp.115-123
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• 1997

In this paper we present a polynomial matrix decomposition algorithm that determines a polynomial matix M(z) which satisfies the relation V(z)=M(z) for a given polynomial matrix V(z) which is paraconjugate hermitian matrix with normal rank r and is positive semidenfinite on the unit circle of z-plane. All the decomposition procedures in this proposed method are performed in the digitral domain. We also discuss how to apply the polynomial matirx decomposition in realizing MIMO LBR two-pairs.

• Bulletin of the Korean Mathematical Society
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• v.42 no.3
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• pp.501-507
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• 2005

A Boolean matrix with rank 1 is factored as a left factor and a right factor. The perimeter of a rank-1 Boolean matrix is defined as the number of nonzero entries in the left factor and the right factor of the given matrix. We obtain new characterizations of rank preservers, in terms of perimeter, of Boolean matrices.

• Journal of applied mathematics & informatics
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• v.29 no.1_2
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• pp.49-53
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• 2011

In this paper, we adopt a numerical method to establish the smallest set to contain all Ger$\v{s}$gorin discs of a given complex matrix and its some similar matrices. With the smallest set, a new estimation for all eigenvalues of the matrix is obtained.

• Communications of the Korean Mathematical Society
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• v.9 no.3
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• pp.753-765
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• 1994

The linearly constrained quadratic programming(QP) considered is : $$ min f(x) = c^T x + \frac{1}{2}x^T Hx $$ $$ (1) subject to A^T x \geq b,$$ where $c,x \in R^n, b \in R^m, H \in R^{n \times n)}$, symmetric, and $A \in R^{n \times n}$. If there are bounds on x, these are included in the matrix $A^T$. The Hessian matrix H may be positive definite or negative semi-difinite. For large problems H and the constraint matrix A are assumed to be sparse.

• Journal of Advanced Navigation Technology
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• v.26 no.3
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• pp.166-171
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• 2022

In this paper, we propose an algorithm to improve DoA(direction of arrival) estimation performance of the subspace-based method by generating high robustness correlation matrix of the signals incident on the uniformly linear array antenna. The existing subspace-based DoA estimation method estimates the DoA by obtaining a correlation matrix and dividing it into a signal subspace and a noise subspace. However, the component of the correlation matrix obtained from the low SNR and small number of snapshots inaccurately estimates the signal subspace due to the noise component of the antenna, thereby degrading the DoA estimation performance. Therefore a robust correlation matrix is generated by arranging virtual signal vectors obtained from the existing correlation matrix in a sliding manner. As a result of simulation using MUSIC and ESPRIT, which are representative subspace-based methods,, the computational complexity increased by less than 2.5% compared to the existing correlation matrix, but both MUSIC and ESPRIT based on RMSE 1° showed superior DoA estimation performance with an SNR of 3dB or more.

• Journal of Ubiquitous Convergence Technology
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• v.2 no.1
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• pp.18-26
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• 2008

The invariance relation existing in the non-negative matrix factorization (NMF) is used for constructing robust image hashes in this work. The image is first re-scaled to a fixed size. Low-pass filtering is performed on the luminance component of the re-sized image to produce a normalized matrix. Entries in the normalized matrix are pseudo-randomly re-arranged under the control of a secret key to generate a secondary image. Non-negative matrix factorization is then performed on the secondary image. As the relation between most pairs of adjacent entries in the NMF's coefficient matrix is basically invariant to ordinary image processing, a coarse quantization scheme is devised to compress the extracted features contained in the coefficient matrix. The obtained binary elements are used to form the image hash after being scrambled based on another key. Similarity between hashes is measured by the Hamming distance. Experimental results show that the proposed scheme is robust against perceptually acceptable modifications to the image such as Gaussian filtering, moderate noise contamination, JPEG compression, re-scaling, and watermark embedding. Hashes of different images have very low collision probability. Tampering to local image areas can be detected by comparing the Hamming distance with a predetermined threshold, indicating the usefulness of the technique in digital forensics.

• Journal of the Korean Society for Heat Treatment
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• v.21 no.1
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• pp.20-25
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• 2008

Structural studies have been performed on precipitation hardening and microstructural variations found in Ti-Al-Cr ternary $L1_0$- and $L1_2$-phase alloys using transmission electron microscopy. Both the $L1_0$ and $L1_2$ phase alloys harden by aging at 973 K after solution annealing at higher temperatures. The amount of age hardening of the $L1_2$ phase alloy is larger than that of the $L1_0$ phase alloy. The phase separation between $L1_0$ and $L1_2$ phase have not been observed by aging at 973 K. But $Al_2Ti$ was formed in each matrix alloy during aging. The crystal structure of the $Al_2Ti$ phase is a $Ga_2Zr$ type in the $L1_0$ and a $Ga_2Hf$ type in the $L1_2$ phase, respectively. At the beginning of aging the fine coherent cuboidal $Al_2Ti$-phase are formed in the $L1_0$ phase. By further aging, two variants of $Al_2Ti$ precipitates grow along the two {110} habit planes. On the other hand, in the $L1_2$ phase, the $Al_2Ti$ phase forms on the {100} planes of the $L1_2$ matrix lattice. After prolonged aging the precipitates are rearranged along a preferential direction of the matrix lattice and form a domain consisting of only one variant. It is suggested that the precipitation of $Al_2Ti$ in each matrix alloy occurs to form a morphology which efficiently relaxes the elastic strain between precipitate and matrix lattices.

• The Mathematical Education
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• v.34 no.1
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• pp.7-9
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• 1995

• Journal of the Korean Data and Information Science Society
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• v.7 no.1
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• pp.79-85
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• 1996

This paper will show that the rank of the model matrix of a closed, n compartmental model with k sinks is n-k. This statement will be extended to include open compartmental models as a part of theorem.