Bulletin of the Korean Mathematical Society (대한수학회보)

Korean Mathematical Society (대한수학회)
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ON THE NONLINEAR MATRIX EQUATION $X+\sum_{i=1}^{m}A_i^*X^{-q}A_i=Q$(0＜q≤1)

  • Yin, Xiaoyan (Department of Mathematics Xidian University) ;
  • Wen, Ruiping (Department of Mathematics Taiyuan Normal University) ;
  • Fang, Liang (Department of Mathematics Xidian University)
  • Received : 2013.03.27
  • Published : 2014.05.31
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Abstract

In this paper, the nonlinear matrix equation $$X+\sum_{i=1}^{m}A_i^*X^{-q}A_i=Q(0<q{\leq}1)$$ is investigated. Some necessary conditions and sufficient conditions for the existence of positive definite solutions for the matrix equation are derived. Two iterative methods for the maximal positive definite solution are proposed. A perturbation estimate and an explicit expression for the condition number of the maximal positive definite solution are obtained. The theoretical results are illustrated by numerical examples.

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References

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