Convergence analysis of the doubling algorithm for several nonlinear matrix equations in the critical case

Chun-Yueh Chiang; King-Wah Eric Chu; Chun-Hua Guo; Tsung-Ming Huang; Wen-wei Lin; Shu-Fang Xu

Convergence analysis of the doubling algorithm for several nonlinear matrix equations in the critical case

Chun-Yueh Chiang, King-Wah Eric Chu, Chun-Hua Guo, Tsung-Ming Huang, Wen-wei Lin, Shu-Fang Xu

School of Mathematics

Research output: Contribution to journal › Article › Research › peer-review

55 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 language	English
Pages (from-to)	227 - 247
Number of pages	21
Journal	SIAM Journal on Matrix Analysis and Applications
Volume	31
Issue number	2
Publication status	Published - 2009

Cite this

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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.",

author = "Chun-Yueh Chiang and Chu, {King-Wah Eric} and Chun-Hua Guo and Tsung-Ming Huang and Wen-wei Lin and Shu-Fang Xu",

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AU - Chiang, Chun-Yueh

AU - Chu, King-Wah Eric

AU - Guo, Chun-Hua

AU - Huang, Tsung-Ming

AU - Lin, Wen-wei

AU - Xu, Shu-Fang

PY - 2009

Y1 - 2009

N2 - 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.

AB - 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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M3 - Article

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SP - 227

EP - 247

JO - SIAM Journal on Matrix Analysis and Applications

JF - SIAM Journal on Matrix Analysis and Applications

IS - 2

ER -

Convergence analysis of the doubling algorithm for several nonlinear matrix equations in the critical case

Abstract

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