• 대한수학회논문집
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• 제34권4호
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• pp.1135-1143
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• 2019

The matrix representation of the Toeplitz operator on the Hardy space with respect to a generalized orthonormal basis for the space of square integrable functions associated to a bounded simply connected region in the complex plane is completely computed in terms of only the Szegő kernel and the Garabedian kernels.

• 한국정보통신학회논문지
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• 제26권11호
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• pp.1623-1629
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• 2022

행렬 곱셈은 과학 및 공학 분야에서 널리 사용되는 기본 연산이다. 딥러닝의 학습 알고리즘에도 행렬 곱셈이 많이 사용된다. 따라서 행렬 곱셈을 효과적으로 수행하기 위한 다양한 알고리즘들 개발하고 있다. 이중 행렬 곱셈의 연산량을 줄이는 방법으로 근사 행렬 곱셈 방법이 있다. 근사 행렬 곱셈은 행렬의 열과 행을 선택하기 위한 적절한 확률 분포를 결정하고, 이 분포에 따라 행렬의 열과 행을 선택하여 근사 행렬 곱셈을 수행한다. 기존의 방법들을 행렬 곱셈에 참여하는 두 개의 행렬 A, B를 모두 고려하여 확률 분포를 생성한다. 본 논문은 행렬 A만을 대상으로 근사 행렬 곱셈에 사용될 행렬의 열과 행을 선택하는 확률 분포를 생성하는 방법을 제안하였다. 기존의 방법들과 제안된 방법들을 사용하여 1000×1000, 2000×2000, 3000×3000, 4000×4000, 5000×5000 행렬에 대하여 근사 행렬 곱셈을 수행하였다. 기존의 방법보다 제안한 방법을 적용한 근사 행렬 곱셈이 평균 0.02%에서 2.34%까지 원래 행렬 곱셈 결과에 더 근접하는 결과를 보였다.

• Journal of Mechanical Science and Technology
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• 제15권8호
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• pp.1090-1096
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• 2001

In this paper, new methods for efficiently solving linear acceleration equations of multibody dynamic simulation exploiting sparsity for real-time simulation are presented. The coefficient matrix of the equations tends to have a large number of zero entries according to the relative joint coordinate numbering. By adequate joint coordinate numbering, the matrix has minimum off-diagonal terms and a block pattern of non-zero entries and can be solved efficiently. The proposed methods, using sparse Cholesky method and recursive block mass matrix method, take advantages of both the special structure and the sparsity of the coefficient matrix to reduce computation time. The first method solves the η$\times$η sparse coefficient matrix for the accelerations, where η denotes the number of relative coordinates. In the second method, for vehicle dynamic simulation, simple manipulations bring the original problem of dimension η$\times$η to an equivalent problem of dimension 6$\times$6 to be solved for the accelerations of a vehicle chassis. For vehicle dynamic simulation, the proposed solution methods are proved to be more efficient than the classical approaches using reduced Lagrangian multiplier method. With the methods computation time for real-time vehicle dynamic simulation can be reduced up to 14 per cent compared to the classical approach.

• 조명전기설비학회논문지
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• 제28권11호
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• pp.93-99
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• 2014

The method of moments is applied to numerically compute the electrostatic capacitance of a parallel-plate rectangular capacitor of finite area. Each plate is discretized into 900 patches per unit area to ensure a high accuracy of computation. To further enhance computational results, the impedance matrix elements are additionally evaluated in the case that the observation patch is located above or below the source patch in the vertical direction. To examine the fringing effect at the edges of the capacitor, the normalized capacitances are computed as a function of separation distance. After these results have been verified by Palmer's formula, this method is extended to the computation of capacitances between two different size plates.

• 대한음성학회:학술대회논문집
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• 대한음성학회 2003년도 5월 학술대회지
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• pp.123-126
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• 2003

We discuss how to reduce the number of inverse matrix and its dimensions requested in MLLR framework for speaker adaptation. To find a smaller set of variables with less redundancy, we employ PCA(principal component analysis) and ICA(independent component analysis) that would give as good a representation as possible. The amount of additional computation when PCA or ICA is applied is as small as it can be disregarded. The dimension of HMM parameters is reduced to about 1/3 ~ 2/7 dimensions of SI(speaker independent) model parameter with which speech recognition system represents word recognition rate as much as ordinary MLLR framework. If dimension of SI model parameter is n, the amount of computation of inverse matrix in MLLR is proportioned to O($n^4$). So, compared with ordinary MLLR, the amount of total computation requested in speaker adaptation is reduced to about 1/80~1/150.

• Journal of applied mathematics & informatics
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• 제28권3_4호
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• pp.987-992
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• 2010

H-matrix is a special class of matrices with wide applications in engineering and scientific computation, how to judge if a given matrix is an H-matrix is very important, especially for large scale matrices. In this paper, we obtain several new practical criteria for judging nonsingular H-matrices by using the partitioning technique and Schur complement of matrices. Their effectiveness is illustrated by numerical examples.

• 한국산업정보학회논문지
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• 제12권2호
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• pp.68-78
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• 2007

D-클래스는 주어진 동치관계(equivalence relation)에 있는 $n{\times}n$ 불리언 행렬의 집합으로 정의된다. D-클래스 계산은 $n{\times}n$ 불리언 행렬의 전체 집합을 대상으로 이 집합에서 조합할 수 있는 모든 세 불리언 행렬 사이의 곱셈을 요구한다. 그러나 불리언 행렬에 대한 대부분의 연구는 단지 두 개의 불리언 행렬에 대한 효율적인 곱셈에 집중되었으며 모든 불리언 행렬 사이의 곱셈에 대한 연구는 최근에야 소수가 보이고 있다. 본 논문은 모든 세 개의 불리언 행렬 곱셈과 모든 D-클래스를 보다 효율적으로 계산할 수 있는 이론을 제시하고 이를 적용한 알고리즘과 실행결과에 대하여 논한다.

• 대한전기학회논문지:전력기술부문A
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• 제54권6호
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• pp.293-305
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• 2005

This paper describes an improved Prony method in its speed, accuracy and reliability by efficiently determining the optimal sampling interval with use of DFT (discrete Fourier transformation). In the Prony method the computation time is dominated by the size of the linear prediction matrix, which is given by the number of data times the modeling order The size of the matrix in a general Prony method becomes large because of large number of data and so does the computation time. It is found that the Prony method produces satisfactory results when SNR is greater than three. The maximum sampling interval resulting minimum computation time is determined using the fact that the spectrum in DFT is inversely proportional to sampling interval. Also the process of computing the modes is made efficient by applying Hessenberg method to the companion matrix with complex shift and computing selectively only the dominant modes of interest. The proposed method is tested against the 2003 KEPCO system and found to be efficient and reliable. The proposed method may play a key role in monitoring in real time low frequency oscillations of power systems .

• ETRI Journal
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• 제31권2호
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• pp.129-139
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• 2009

This paper provides an efficient algorithm for computing the ${\eta}_T$ pairing on supersingular elliptic curves over fields of characteristic two. In the proposed algorithm, we deploy a modified multiplication in $F_{2^{4n}}$ using the Vandermonde matrix. For F, G ${\in}$ $F_{2^{4n}}$ the proposed multiplication method computes ${\beta}{\cdot}F{\cdot}G$ instead of $F{\cdot}G$ with some ${\beta}$ ${\in}$ $F^*_{2n}$ because ${\beta}$ is eliminated by the final exponentiation of the ${\eta}_T$ pairing computation. The proposed multiplication method asymptotically requires only 7 multiplications in $F_{2^n}$ as n ${\rightarrow}$ ${\infty}$, while the cost of the previously fastest Karatsuba method is 9 multiplications in $F_{2^n}$. Consequently, the cost of the ${\eta}_T$ pairing computation is reduced by 14.3%.

• Journal of applied mathematics & informatics
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• 제24권1_2호
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• pp.81-94
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• 2007

In this paper we investigate symbolic implementation of two modifications of the Leverrier-Faddeev algorithm, which are applicable in computation of the Moore-Penrose and the Drazin inverse of rational matrices. We introduce an algorithm for computation of the Drazin inverse of rational matrices. This algorithm represents an extension of the papers [11] and [14]. and a continuation of the papers [15, 16]. The symbolic implementation of these algorithms in the package MATHEMATICA is developed. A few matrix equations are solved by means of the Drazin inverse and the Moore-Penrose inverse of rational matrices.