• East Asian mathematical journal
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• 제29권5호
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• pp.511-519
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• 2013

There are various methods for evaluating a matrix square root, which is a solvent of the quadratic matrix equation $X^2-A=0$. We consider new iterative methods for solving matrix square roots of M-matrices. Particulary we show that the relaxed binomial iteration is more efficient than Newton-Schulz iteration in some cases. And we construct a formula to find relaxation coefficients through statistical experiments.

• Journal of applied mathematics & informatics
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• 제11권1_2호
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• pp.401-412
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• 2003

Using the idea of "intuitionistic fuzzy set" [l, 2, 3], we defined the concept of intuitionistic fuzzy matrices as a natural generalization of fuzzy matrices. And we introduced and studied the determinant of square intuitionistic fuzzy matrices [4]. In this paper, we investigate the adjoint of square intuitionistic fuzzy matrices.

• KSII Transactions on Internet and Information Systems (TIIS)
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• 제13권11호
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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.

• East Asian mathematical journal
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• 제39권5호
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• pp.523-528
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• 2023

Let S_n = [S(i, j)]_1≤i,j≤n and S^*_n = [S(i + j, j)]_1≤i,j≤n where S(i, j) is the Stirling number of the second kind. Choi and Jo [On the determinants of the square-type Stirling matrix and Bell matrix, Int. J. Math. Math. Sci. 2021] obtained the diagonal entries of matrix U in the LU-factorization of S^*_n for calculating the determinant of S^*_n, where L = S_n. In this paper, we compute the all entries of U in the LU-factorization of matrix S^*_n. This implies the identities related to Stirling numbers of both kinds.

• 대한수학회지
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• 제36권4호
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• pp.773-785
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• 1999

Shifts of finite type are represented by nonnegative integral square matrics, and conjugacy between two shifts of finite type is determined by strong shift equivalence between the representing nonnegative intergral square matrices. But determining strong shift equivalence is usually a very difficult problem. we develop splittings and amalgamations of nonnegative integral matrices, which are analogues of those of directed graphs, and show that two nonnegative integral square matrices are strong shift equivalent if and only if one is obtained from a higher matrix of the other matrix by a series of amalgamations.

• 한국정보전자통신기술학회논문지
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• 제11권6호
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• pp.691-696
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• 2018

We propose an algorithm to update weight to use the mean square error method and mutual coupling matrix in a coherent channel. The algorithm proposed in this paper estimates the desired signal by using the updated weight. The updated weight is obtained by covariance matrix using mean square error and mutual coupling matrix. The MUSIC algorithm, which is direction of arrival estimation method, is mostly used in the desired signal estimation. The MUSIC algorithm has a good resolution because it uses subspace techniques. The proposed method estimates the desired signal by updating the weights using the mutual coupling matrix and mean square error method. Through simulation, we analyze the performance by comparing the classical MUSIC and the proposed algorithm in a coherent channel. In this case of the coherent channel for estimating at the three targets (-10o, 0o, 10o), the proposed algorithm estimates all the three targets (-10o, 0o, 10o). But the classical MUSIC algorithm estimates only one target (x, x, 10o). The simulation results indicate that the proposed method is superior to the classical MUSIC algorithm for desired signal estimation.

• 소음진동
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• 제6권5호
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• pp.679-684
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• 1996

The Instrumental Variable Method(IVM), modified from least square algorithm, is applied to parameter identification of a noise contaminated bearing test rig. The signal to noise ratio included in Frequency Response Function(FRF) can cause significant errors in parameter identification. Therefore, among several candidates of parameter identification method, results of the applied IVM were compared with noise-contaminated least square method. This study shows that the noise-contaminated least square method can have indonsistent accuracy depending on the degree of noise level, while the IVM has robuster performance to signal to noise ratio than least square method.

• 대한수학회보
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• 제48권4호
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• pp.725-736
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• 2011

By using the Lyapunov functional method, stochastic analysis, and LMI (linear matrix inequality) approach, the mean square exponential stability of an equilibrium solution of uncertain stochastic Hopfield neural networks with delayed is presented. The proposed result generalizes and improves previous work. An illustrative example is also given to demonstrate the effectiveness of the proposed result.

• 한국통신학회논문지
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• 제37권6A호
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• pp.488-496
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• 2012

본 논문에서는 간섭을 정렬시키는 조건을 선형 결합하고 채널과 빔형성 벡터로 행렬화하여 간섭을 제어하고자 한다. 또한 선형 결합 계수를 갱신함으로써 최적의 빔형성 벡터를 찾고자 한다. 이는 기존의 최소 제곱 기반의 간섭 정렬과 비슷한 형태를 가지지만 행렬화하는 과정을 단순화시켜 곱셈 연산을 없앴기 때문에 직관적으로도 충분히 해결할 수 있다는 장점을 가지고 있다. 모의실험 결과 제안하는 기법이 기존의 최소 제곱 기반의 간섭 정렬 기법보다 4bps/Hz정도의 이득을 가졌으며, 송수신 안테나 수가 증가하여도 이에 따른 행렬의 크기가 기존 기법보다 줄어들기 때문에 곱셈 연산이 증가하지 않아 복잡도가 낮아짐을 확인하였다.

• Journal of the Korean Physical Society
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• 제73권12호
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• pp.1808-1813
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• 2018

I develop a transfer matrix algorithm for computing the geometric quantities of a square lattice polymer with nearest-neighbor interactions. The radius of gyration, the end-to-end distance, and the monomer-to-end distance were computed as functions of the temperature. The computation time scales as ${\lesssim}1.8^N$ with a chain length N, in contrast to the explicit enumeration where the scaling is ${\sim}2.7^N$. Various techniques for reducing memory requirements are implemented.