Convergence Analysis of the Doubling Algorithm for Several Nonlinear Matrix Equations in the Critical Case

@article{Chiang2009ConvergenceAO,
  title={Convergence Analysis of the Doubling Algorithm for Several Nonlinear Matrix Equations in the Critical Case},
  author={Chun-Yueh Chiang and Eric King-wah Chu and Chun-Hua Guo and Tsung-Ming Huang and Wen-Wei Lin and Shufang Xu},
  journal={SIAM J. Matrix Anal. Appl.},
  year={2009},
  volume={31},
  pages={227-247}
}
In this paper, we review two types of doubling algorithm and some techniques for analyzing them. We then use the techniques to study the doubling algorithm for three different nonlinear matrix equations in the critical case. We show that the convergence of the doubling algorithm is at least linear with rate $1/2$. As compared to earlier work on this topic, the results we present here are more general, and the analysis here is much simpler. 
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