• East Asian mathematical journal
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• v.29 no.5
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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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• v.11 no.1_2
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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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• 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.

• East Asian mathematical journal
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• v.39 no.5
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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.

• Journal of the Korean Mathematical Society
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• v.36 no.4
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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.

• The Journal of Korea Institute of Information, Electronics, and Communication Technology
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• v.11 no.6
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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.

• Journal of KSNVE
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• v.6 no.5
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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.

• Bulletin of the Korean Mathematical Society
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• v.48 no.4
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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.

• The Journal of Korean Institute of Communications and Information Sciences
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• v.37 no.6A
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• pp.488-496
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• 2012

In this paper, the scheme for designing optimal beamforming matrix for interference control is proposed. The optimal beamforming matrix is found though linear combination of interference alignment conditions and renewal of linear combination coefficient. The proposed scheme has advantages that the complexity is reduced and there is no multiplying operation in matrix calculations even if proposed scheme has the form similar to that of existing least square based scheme. The simulation results show that proposed scheme has about 4bps/Hz higher gain than existing least square scheme. Also there is no additional multiplying calculation and increase of matrix size when the number of transmit and receive antennas is increased.

• Journal of the Korean Physical Society
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• v.73 no.12
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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.