• Journal of applied mathematics & informatics
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• 제26권3_4호
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• pp.471-479
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• 2008

Let $R\;{\in}\;C^{m{\times}m}$ and $S\;{\in}\;C^{n{\times}n}$ be nontrivial unitary involutions, i.e., $R^*\;=\;R\;=\;R^{-1}\;{\neq}\;I_m$ and $S^*\;=\;S\;=\;S^{-1}\;{\neq}\;I_m$. We say that $G\;{\in}\;C^{m{\times}n}$ is a generalized reflexive matrix if RGS = G. The set of all m ${\times}$ n generalized reflexive matrices is denoted by $GRC^{m{\times}n}$. In this paper, an efficient method for the least squares solution $X\;{\in}\;GRC^{m{\times}n}$ of the matrix equation AXB = D with arbitrary coefficient matrices $A\;{\in}\;C^{p{\times}m}$, $B\;{\in}\;C^{n{\times}q}$and the right-hand side $D\;{\in}\;C^{p{\times}q}$ is developed based on the canonical correlation decomposition(CCD) and, an explicit formula for the general solution is presented.

• Journal of applied mathematics & informatics
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• 제27권5_6호
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• pp.1061-1071
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• 2009

For real generalized reflexive matrices R, S, i.e., $R^T$ = R, $R^2$ = I, $S^T$ = S, $S^2$ = I, we say that real matrix X is (R,S)-symmetric, if RXS = X. In this paper, an iterative algorithm is proposed to solve the least-squares problem of matrix equation AXB = C with (R,S)-symmetric X. Furthermore, the optimal approximation solution to given matrix $X_0$ is also derived by this iterative algorithm. Finally, given numerical example and its convergent curve show that this method is feasible and efficient.

• 대한토목학회논문집
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• 제10권3호
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• pp.57-65
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• 1990

2절점 유한 요소법을 사용하여 비보존력을 받는 평면뼈대 구조물의 안정성문제를 취급하였다. 포물선 분포를 이루는 축방향력에 대한 가하적인 강도매트럭스, 비보존력의 방향변화를 고려하는 load correction stiffness matrix 그리고 내적 몇 외적감쇠효과를 고려하는 감쇠매트릭스들을 산정하고 이들을 고려한 매트릭스 운동방정식을 유도하였다. 이 방정식으로부터 얻어지는 고유치 문제들을 분석하므로써 감쇠하중의 영향이 고려된 비보존력계의 동적(動的) 안정성(安定性)을 조사하였다. 문헌들에서 취급된 예제들의 해석결과들과 본연구에 의한 결과들을 비교 분석하므로써 본 논문에서 제시한 이론의 정당성을 입증하였다.

• 제어로봇시스템학회논문지
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• 제18권9호
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• pp.806-811
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• 2012

In this paper Hartley functions are used to approximate the solutions of continuous time linear dynamical system. The Hartley function and its integral operational matrix are first presented, an efficient algorithm to solve the Stein equation is proposed. The algorithm is based on the compound matrix and the inverse of sum of matrices. Using the structure of the Hartley's integral operational matrix, the full order Stein equation should be solved in terms of the solutions of pure algebraic matrix equations, which reduces the computation time remarkably. Finally a numerical example is illustrated to demonstrate the validity of the proposed algorithm.

• 대한수학회논문집
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• 제39권3호
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• pp.785-802
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• 2024

Given M a monoid with a neutral element e. We show that the solutions of d'Alembert's functional equation for n × n matrices Φ(pr, qs) + Φ(sp, rq) = 2Φ(r, s)Φ(p, q), p, q, r, s ∈ M are abelian. Furthermore, we prove under additional assumption that the solutions of the n-dimensional mixed vector-matrix Wilson's functional equation $$\begin{cases}f(pr, qs) + f(sp, rq) = 2\phi(r, s)f(p, q),\\Φ(p, q) = \phi(q, p),{\quad}p, q, r, s {\in} M\end{cases}$$ are abelian. As an application we solve the first functional equation on groups for the particular case of n = 3.

• 대한수학회보
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• 제55권2호
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• pp.431-448
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• 2018

This paper is concerned with the positive definite solutions of the nonlinear matrix equation $X-A^*{\bar{X}}^{-1}A=Q$, where A, Q are given complex matrices with Q positive definite. We show that such a matrix equation always has a unique positive definite solution and if A is nonsingular, it also has a unique negative definite solution. Moreover, based on Sherman-Morrison-Woodbury formula, we derive elegant relationships between solutions of $X-A^*{\bar{X}}^{-1}A=I$ and the well-studied standard nonlinear matrix equation $Y+B^*Y^{-1}B=Q$, where B, Q are uniquely determined by A. Then several effective numerical algorithms for the unique positive definite solution of $X-A^*{\bar{X}}^{-1}A=Q$ with linear or quadratic convergence rate such as inverse-free fixed-point iteration, structure-preserving doubling algorithm, Newton algorithm are proposed. Numerical examples are presented to illustrate the effectiveness of all the theoretical results and the behavior of the considered algorithms.

• Journal of applied mathematics & informatics
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• 제12권1_2호
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• pp.165-182
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• 2003

Toeplitz matrix method and the product Nystrom method are described for mixed Fredholm-Volterra singular integral equation of the second kind with Carleman Kernel and logarithmic kernel. The results are compared with the exact solution of the integral equation. The error of each method is calculated.

• 전기전자학회논문지
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• 제23권2호
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• pp.614-621
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• 2019

본 논문은 integral equation-fast Fourier transform(IE-FFT)과 block matrix preconditioner(BMP)를 이용하여 침투 가능한 구조물의 전자기 산란 문제를 다룬다. IE-FFT는 모멘트 법(the method of Moments : MoM)에 의해 형성된 행렬방정식의 해를 계산하기 위하여 반복법의 연산량을 상당히 개선할 수 있다. 또한 전기적으로 커다란 구조물로부터 형성된 행렬방정식에 BMP가 적용된 반복법을 적용하면 반복 횟수를 크게 줄여 행렬방정식의 해를 빠르게 계산할 수 있다. 수치해석 결과는 IE-FFT와 BMP를 적용하여 침투 가능한 구조물의 전자기 산란 문제를 빠르고 정확하게 계산할 수 있음을 보여준다.

• 대한수학회지
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• 제50권4호
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• pp.755-770
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• 2013

One of the interesting nonlinear matrix equations is the quadratic matrix equation defined by $$Q(X)=AX^2+BX+C=0$$, where X is a $n{\times}n$ unknown real matrix, and A, B and C are $n{\times}n$ given matrices with real elements. Another one is the matrix polynomial $$P(X)=A_0X^m+A_1X^{m-1}+{\cdots}+A_m=0,\;X,\;A_i{\in}\mathbb{R}^{n{\times}n}$$. Newton's method is used to find the symmetric and bisymmetric solvents of the nonlinear matrix equations Q(X) and P(X). The method does not depend on the singularity of the Fr$\acute{e}$chet derivative. Finally, we give some numerical examples.

• International Journal of Control, Automation, and Systems
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• 제6권5호
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• pp.776-784
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• 2008

In this paper, new upper matrix bounds for the solution of the continuous algebraic Riccati equation (CARE) are derived. Following the derivation of each bound, iterative algorithms are developed for obtaining sharper solution estimates. These bounds improve the restriction of the results proposed in a previous paper, and are more general. The proposed bounds are always calculated if the stabilizing solution of the CARE exists. Finally, numerical examples are given to demonstrate the effectiveness of the present schemes.