Journal of applied mathematics & informatics

The Korean Society for Computational and Applied Mathematics (한국전산응용수학회)
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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)
  • Received : 2011.08.24
  • Accepted : 2011.12.05
  • Published : 2012.05.30
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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.

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References

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