논문KCI 등재
Perturbation anaysis for the matrix equation X=I-A*X-1A+B*X-1B
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The purpose of this paper is to study the perturbation analysis of the matrix equation X=I-A*X-1A+B*X-1B. Based on the matrix differentiation, we give a precise perturbation bound for the positive definite solution. A numerical example is presented to illustrate the shrpness of the perturbation bound.
Abstract
The purpose of this paper is to study the perturbation analysis of the matrix equation X=I-A*X-1A+B*X-1B. Based on the matrix differentiation, we give a precise perturbation bound for the positive definite solution. A numerical example is presented to illustrate the shrpness of the perturbation bound.
참고문헌 (10)
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- T.G. Bhaskar, "Fixed point theorems in partially ordered metric spaces and applications", Nonlinear Anal, 65, pp.13791393~ (2006)
- X. Duan, "Perturbation analysis for the matrix equation X - ∑mi=1A∗iXAi+∑nj=1B∗jXBj∑i=1mAi∗XAi+∑j=1nBj∗XBj = I", J. Appl. Math (2012)
- J.C. Engwerda, "Necessary and sufficient conditions for the existence of a positive definite solution of the matrix equation X + A∗X−1AA∗X−1A = Q.", Linear Algebra Appl, 186, pp.255~275 (1993)
- B.R. Fang, "Matrix Theory" (2006), Tsinghua University Press
- A. Ferrante, "Hermitian solutions of the equations X = Q + NX−1N∗NX−1N∗", Linear Algebra Appl, 247, pp.359~373 (1996)
- V.I. Hasanov, "Positive definite solutions of the matrix equations X±A∗X−qAX±A∗X−qA = Q", Linear Algebra Appl, 404, pp.166~182 (2005)
- T.P. Minka, "Old and new matrix algebra useful for statistics", December 2000. Notes, ~ (2000)
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