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http://dx.doi.org/10.14317/jami.2012.30.3_4.655

PERTURBATION ANALYSIS FOR THE POSITIVE DEFINITE SOLUTION OF THE NONLINEAR MATRIX EQUATION $X-\sum^m_{i=1}A^{\ast}_iX^{\delta_i}A_i=Q$  

Duan, Xue-Feng (College of Mathematics and Computational Science, Guilin University of Electronic Technology)
Wang, Qing-Wen (Department of Mathematics, Shanghai University)
Li, Chun-Mei (College of Mathematics and Computational Science, Guilin University of Electronic Technology)
Publication Information
Journal of applied mathematics & informatics / v.30, no.3_4, 2012 , pp. 655-663 More about this Journal
Abstract
Based on the elegant properties of the spectral norm and Thompson metric, we firstly give two perturbation estimates for the positive definite solution of the nonlinear matrix equation $$X-\sum^m_{i=1}A^{\ast}_iX^{\delta_i}A_i=Q(0<|{\delta}_i|<1)$$ which arises in an optimal interpolation problem.
Keywords
Nonlinear matrix equation; Positive definite solution; Perturbation estimate; Spectral norm; Thompson metric;
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