Convergence analysis of the doubling algorithm for several nonlinear matrix equations in the critical case

Chun Yueh Chiang, Eric King Wah Chu, Chun Hua Guo, Tsung Ming Huang, Wen Wei Lin, Shu Fang Xu

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44 Citations (Scopus)

Abstract

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.

Original languageEnglish
Pages (from-to)227-247
Number of pages21
JournalSIAM Journal on Matrix Analysis and Applications
Volume31
Issue number2
DOIs
Publication statusPublished - 2009 Dec 28

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Keywords

  • Convergence rate
  • Critical case
  • Cyclic reduction
  • Doubling algorithm
  • Maximal positive definite solution
  • Minimal nonnegative solution
  • Nonlinear matrix equation

ASJC Scopus subject areas

  • Analysis

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