Title: CONVERGENCE ANALYSIS OF THE DOUBLING ALGORITHM FOR SEVERAL NONLINEAR MATRIX EQUATIONS IN THE CRITICAL CASE
Authors: Chiang, Chun-Yueh
Chu, Eric King-Wah
Guo, Chun-Hua
Huang, Tsung-Ming
Lin, Wen-Wei
Xu, Shu-Fang
應用數學系
Department of Applied Mathematics
Keywords: nonlinear matrix equation;minimal nonnegative solution;maximal positive definite solution;critical case;doubling algorithm;cyclic reduction;convergence rate
Issue Date: 2009
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.
URI: http://hdl.handle.net/11536/7834
http://dx.doi.org/10.1137/080717304
ISSN: 0895-4798
DOI: 10.1137/080717304
Journal: SIAM JOURNAL ON MATRIX ANALYSIS AND APPLICATIONS
Volume: 31
Issue: 2
Begin Page: 227
End Page: 247
Appears in Collections:Articles


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