• 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.

• 제어로봇시스템학회:학술대회논문집
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• 제어로봇시스템학회 1989년도 한국자동제어학술회의논문집; Seoul, Korea; 27-28 Oct. 1989
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• pp.461-466
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• 1989

This paper describes some properties of a discrete algebraic Riccati equation and its application to $H^{\infty}$ control design. The conditions, under which an input weighting matrix can be found for a negative output weighting matrix in order that a solution P for a discrete algebraic equation may exist, are suggested in case of a stable A. This result is applied to a $H^{\infty}$ controller design for the special case of nonsingular B. It is based on a state feedback control law whose objective is to reduce the effect of input disterbances below a prespecified level. This law requires the solution of a modified algebraic Riccati equation, which provides an method for the $H^{\infty}$ optimization control problem approximately.ly.

• 응용통계연구
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• 제4권1호
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• pp.1-11
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• 1991

다변량분산분석이나 판별분석 등에 있어서 검정의 대상이 되는 공분산행렬의 동일성에 대한 붓스트랩방법의 활용을 살펴보았다. 두 모집단의 공분산행렬을 $\Sigma_1, \Sigma_2^$라 하면, 가설 H : $\Sigma_1 = \Sigma_2$은 불변성의 관점에서 $\Sigma = \Sigma_1 \Sigma_2^{-1}$의 고유값들이 모두 1 이라는 것과 동등하다. 본 연구에서는 (1) $\Sigma = \Sigma_1 \Sigma_2^{-1}$의 표본고유값들에 대한 편의를 붓스트랩에 의해 정정하였으며, (2) 이들의 표본분포를 붓스트랩분포로 추정하여 검정에 활용하였으며, (3) 합동붓스트랩에 의해 바플렛의 수정우도비 검정통계량의 분포를 근사하였다.