Convergence Analysis of the Doubling Algorithm for Several Nonlinear Matrix Equations in the Critical Case
SIAM Journal on Matrix Analysis and Applications2009Vol. 31(2), pp. 227–247
Citations Over TimeTop 10% of 2009 papers
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.
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