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

Research output: Contribution to journalArticle

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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Nonlinear Matrix Equation
Critical Case
Doubling
Convergence Analysis

Keywords

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

ASJC Scopus subject areas

  • Analysis

Cite this

Convergence analysis of the doubling algorithm for several nonlinear matrix equations in the critical case. / Chiang, Chun Yueh; Chu, Eric King Wah; Guo, Chun Hua; Huang, Tsung Ming; Lin, Wen Wei; Xu, Shu Fang.

In: SIAM Journal on Matrix Analysis and Applications, Vol. 31, No. 2, 28.12.2009, p. 227-247.

Research output: Contribution to journalArticle

Chiang, Chun Yueh ; Chu, Eric King Wah ; Guo, Chun Hua ; Huang, Tsung Ming ; Lin, Wen Wei ; Xu, Shu Fang. / Convergence analysis of the doubling algorithm for several nonlinear matrix equations in the critical case. In: SIAM Journal on Matrix Analysis and Applications. 2009 ; Vol. 31, No. 2. pp. 227-247.
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