Perturbation bounds for the nonlinear matrix equation X + A H X -1 A + B H X -1 B = I

作者: Ivan Popchev , Petko Petkov , Mihail Konstantinov , Vera Angelova

DOI: 10.1007/978-3-642-29843-1_17

关键词:

摘要: In this paper we make a complete perturbation analysis of the nonlinear matrix equation, where A and B are square complex matrices, denotes conjugate transpose I is identity matrix. We obtain local (first order) bounds non-local bound for solution to equation. The allow derive condition accuracy estimates computed solution, when using stable numerical algorithm solve

参考文章(7)
V. Mehrmann, D. Gu, M. Konstantinov, P. Petkov, Perturbation Theory for Matrix Equations ,(2003)
Vejdi I. Hasanov, Notes on two perturbation estimates of the extreme solutions to the equations X±A*X -1 A=Q Applied Mathematics and Computation. ,vol. 216, pp. 1355- 1362 ,(2010) , 10.1016/J.AMC.2010.02.044
Mihail Konstantinov, Petko Petkov, THE METHOD OF SPLITTING OPERATORS AND LYAPUNOV MAJORANTS IN PERTURBATION LINEAR ALGEBRA AND CONTROL Numerical Functional Analysis and Optimization. ,vol. 23, pp. 529- 572 ,(2002) , 10.1081/NFA-120014751
V.I. Hasanov, I.G. Ivanov, On two perturbation estimates of the extreme solutions to the equations X±A*X−1A=Q Linear Algebra and its Applications. ,vol. 413, pp. 81- 92 ,(2006) , 10.1016/J.LAA.2005.08.013
Jian-hui Long, Xi-yan Hu, Lei Zhang, On the Hermitian positive defnite solution of the nonlinear matrix equation X + A*X−1A + B*X−1B = I Bulletin of The Brazilian Mathematical Society. ,vol. 39, pp. 371- 386 ,(2008) , 10.1007/S00574-008-0011-7
You-mei He, Jian-hui Long, On the Hermitian positive definite solution of the nonlinear matrix equation X+∑i=1mAi∗X-1Ai=I☆ Applied Mathematics and Computation. ,vol. 216, pp. 3480- 3485 ,(2010) , 10.1016/J.AMC.2010.04.041
J H Long, X Y Hu, L Zhang, ON THE HERMITIAN POSITIVE DEFINITE SOLUTION OF THE NONLINEAR MATRIX EQUATION X + A∗ 1 X−1A1 + A∗ 2 X−1A2 = I BULLETIN OF THE BRAZILIAN MATHEMATICAL SOCIETY. ,vol. 222, pp. 645- 654 ,(2008)