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

Date
2009
Authors
Chiang, Chun-Yueh
Chu, Eric King-Wah
Guo, Chun-Hua
Huang, Tsung-Ming
Lin, Wen-Wei
Xu, Shu-Fang
Journal Title
Journal ISSN
Volume Title
Publisher
SIAM
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.

Description
Keywords
Citation
SIAM J. Matrix Anal. Appl.
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