@article{81063af8f8994670a9322a4d7e369cea,
title = "Convergence analysis of the doubling algorithm for several nonlinear matrix equations in the critical case",
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.",
keywords = "Convergence rate, Critical case, Cyclic reduction, Doubling algorithm, Maximal positive definite solution, Minimal nonnegative solution, Nonlinear matrix equation",
author = "Chiang, {Chun Yueh} and Chu, {Eric King Wah} and Guo, {Chun Hua} and Huang, {Tsung Ming} and Lin, {Wen Wei} and Xu, {Shu Fang}",
year = "2009",
doi = "10.1137/080717304",
language = "English",
volume = "31",
pages = "227--247",
journal = "SIAM Journal on Matrix Analysis and Applications",
issn = "0895-4798",
publisher = "Society for Industrial and Applied Mathematics Publications",
number = "2",
}