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

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

doi:10.1137/080717304

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

Chun Yueh Chiang^*, Eric King Wah Chu, Chun Hua Guo, Tsung Ming Huang, Wen Wei Lin, Shu Fang Xu

^*Corresponding author for this work

Department of Mathematics

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

52 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
DOIs	https://doi.org/10.1137/080717304
Publication status	Published - 2009

Keywords

Convergence rate
Critical case
Cyclic reduction
Doubling algorithm
Maximal positive definite solution
Minimal nonnegative solution
Nonlinear matrix equation

ASJC Scopus subject areas

Analysis

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10.1137/080717304

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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.",

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}",

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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.

KW - Convergence rate

KW - Critical case

KW - Cyclic reduction

KW - Doubling algorithm

KW - Maximal positive definite solution

KW - Minimal nonnegative solution

KW - Nonlinear matrix equation

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

Abstract

Keywords

ASJC Scopus subject areas

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