• Journal of applied mathematics & informatics
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• 제17권1_2_3호
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• pp.585-590
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• 2005

An efficient procedure for finding the inverse of a nonsingular matrix is developed by solving directly for the UL decomposition of the inverse based on the entries of the original nonsingular matrix.

• Wind and Structures
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• 제39권2호
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• pp.125-140
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• 2024

The simulation of non-stationary wind velocity is particularly crucial for the wind resistant design of slender structures. Recently, some data-driven simulation methods have received much attention due to their straightforwardness. However, as the number of simulation points increases, it will face efficiency issues. Under such a background, in this paper, a time-varying coherence matrix decomposition method based on Diagonal Proper Orthogonal Decomposition (DPOD) interpolation is proposed for the data-driven simulation of non-stationary wind velocity based on S-transform (ST). Its core idea is to use coherence matrix decomposition instead of the decomposition of the measured time-frequency power spectrum matrix based on ST. The decomposition result of the time-varying coherence matrix is relatively smooth, so DPOD interpolation can be introduced to accelerate its decomposition, and the DPOD interpolation technology is extended to the simulation based on measured wind velocity. The numerical experiment has shown that the reconstruction results of coherence matrix interpolation are consistent with the target values, and the interpolation calculation efficiency is higher than that of the coherence matrix time-frequency interpolation method and the coherence matrix POD interpolation method. Compared to existing data-driven simulation methods, it addresses the efficiency issue in simulations where the number of Cholesky decompositions increases with the increase of simulation points, significantly enhancing the efficiency of simulating multivariate non-stationary wind velocities. Meanwhile, the simulation data preserved the time-frequency characteristics of the measured wind velocity well.

• International Journal of Automotive Technology
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• 제2권3호
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• pp.117-122
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• 2001

For a dynamic analysis of a constrained multibody system, it is necessary to have a routine for satisfying kinematic constraints. LU decomposition scheme, which is used to divide coordinates into dependent and independent coordinates, is efficient but has great difficulty near the singular configuration. Other method such as the projection matrix, which is more stable near a singular configuration, takes longer simulation time due to the large amount of calculation for decomposition. In this paper, the row space and the null space of the Jacobian matrix are proposed by using the pseudo-inverse method and the projection matrix. The equations of the motion of a system are replaced with independent acceleration components using the null space of the Jacobian matrix. Also a new hybrid method is proposed, combining the LU decomposition and the projection matrix. The proposed hybrid method has following advantages. (1) The simulation efficiency is preserved by the LU method during the simulation. (2) The accuracy of the solution is also achieved by the projection method near the singular configuration.

• 전자공학회논문지S
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• 제34S권1호
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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.

• East Asian mathematical journal
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• 제37권3호
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• pp.295-305
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• 2021

In this paper, we analyze the efficiency of a domain decomposition method for the two-dimensional telegraph equations. We formulate the theoretical spectral radius of the iteration matrix generated by the domain decomposition method, because the rate of convergence of an iterative algorithm depends on the spectral radius of the iteration matrix. The theoretical spectral radius is confirmed by the experimental one using MATLAB. Speedup and operation ratio of the domain decomposition method are also compared as the two measurements of the efficiency of the method. Numerical results support the high efficiency of the domain decomposition method.

• KSII Transactions on Internet and Information Systems (TIIS)
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• 제18권4호
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• pp.1020-1041
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• 2024

With the development of covert communication technologies, the number of covert communication technologies using blockchain as a carrier is increasing. However, using the transaction amount of digital currency as a carrier for covert communication has problems such as low embedding rate, large consumption of transaction amount, and easy detection. In this paper, firstly, by experimentally analyzing the distribution of bitcoin transaction amounts, we determine the most suitable range of amounts for matrix decomposition. Secondly, we design a novel matrix decomposition method that can successfully decompose a large amount matrix into two small amount matrices and utilize the elements in the small amount matrices for covert communication. Finally, we analyze the feasibility of the novel matrix decomposition method in this scheme in detail from four aspects, and verify it by experimental comparison, which proves that our scheme not only improves the embedding rate and reduces the consumption of transaction amount, but also has a certain degree of resistance to detection.

• ETRI Journal
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• 제36권1호
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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.

• 대한수학회논문집
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• 제29권2호
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• pp.227-237
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• 2014

For an $m{\times}n$ nonnegative integral matrix A, a generalized inverse of A is an $n{\times}m$ nonnegative integral matrix G satisfying AGA = A. In this paper, we characterize nonnegative integral matrices having generalized inverses using the structure of nonnegative integral idempotent matrices. We also define a space decomposition of a nonnegative integral matrix, and prove that a nonnegative integral matrix has a generalized inverse if and only if it has a space decomposition. Using this decomposition, we characterize nonnegative integral matrices having reflexive generalized inverses. And we obtain conditions to have various types of generalized inverses.

• Communications for Statistical Applications and Methods
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• 제20권3호
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• pp.235-240
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• 2013

Generalized linear mixed models(GLMMs) are frequently used for the analysis of longitudinal categorical data when the subject-specific effects is of interest. In GLMMs, the structure of the random effects covariance matrix is important for the estimation of fixed effects and to explain subject and time variations. The estimation of the matrix is not simple because of the high dimension and the positive definiteness; subsequently, we practically use the simple structure of the covariance matrix such as AR(1). However, this strong assumption can result in biased estimates of the fixed effects. In this paper, we introduce Bayesian modeling approaches for the random effects covariance matrix using a modified Cholesky decomposition. The modified Cholesky decomposition approach has been used to explain a heterogenous random effects covariance matrix and the subsequent estimated covariance matrix will be positive definite. We analyze metabolic syndrome data from a Korean Genomic Epidemiology Study using these methods.

• 한국인터넷방송통신학회논문지
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• 제15권5호
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• pp.39-49
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• 2015

Jacket Matrices: Construction and Its Application for Fast Cooperative Wireless signal Processing[27]에 소개된 Jacket 행렬로부터 일반화된 의사 Jacket 행렬에 대한 특성과 생성에 관한 정리가 발표됐다. 본 논문에서는 MIMO 채널과 같이 $2{\times}4$, $3{\times}6$ 같은 비정방 행렬에서의 의사 Jacket 역행렬에 대한 예제를 제안했다. 또한 의사 MIMO 특이값 분해 (SVD, Singular Value Decomposition) channel을 추론하여 적용하였으며 안테나 어레이를 분할하여 추정하는 채널을 기반으로 SVD를 활용하는데 적용하였다. 이것은 MIMO 채널 및 고유값 분해 (EVD, Eigen Value decomposition) 등에 사용할 수 있다.