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

數學系

研究成果: 雜誌貢獻 › 文章

44 引文斯高帕斯（Scopus）

摘要

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.

原文	英語
頁（從 - 到）	227-247
頁數	21
期刊	SIAM Journal on Matrix Analysis and Applications
卷	31
發行號	2
DOIs	https://doi.org/10.1137/080717304
出版狀態	已發佈 - 2009 十二月 28

ASJC Scopus subject areas

Analysis

存取文件

10.1137/080717304

指紋深入研究「Convergence analysis of the doubling algorithm for several nonlinear matrix equations in the critical case」主題。共同形成了獨特的指紋。

引用此

Chiang, C. Y., Chu, E. K. W., Guo, C. H., Huang, T. M., Lin, W. W., & Xu, S. F. (2009). Convergence analysis of the doubling algorithm for several nonlinear matrix equations in the critical case. SIAM Journal on Matrix Analysis and Applications, 31(2), 227-247. https://doi.org/10.1137/080717304

@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",

month = dec,

day = "28",

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",

}

TY - JOUR

T1 - Convergence analysis of the doubling algorithm for several nonlinear matrix equations in the critical case

AU - Chiang, Chun Yueh

AU - Chu, Eric King Wah

AU - Guo, Chun Hua

AU - Huang, Tsung Ming

AU - Lin, Wen Wei

AU - Xu, Shu Fang

PY - 2009/12/28

Y1 - 2009/12/28

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

UR - http://www.scopus.com/inward/record.url?scp=71949125302&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=71949125302&partnerID=8YFLogxK

U2 - 10.1137/080717304

DO - 10.1137/080717304

M3 - Article

AN - SCOPUS:71949125302

VL - 31

SP - 227

EP - 247

JO - SIAM Journal on Matrix Analysis and Applications

JF - SIAM Journal on Matrix Analysis and Applications

SN - 0895-4798

IS - 2

ER -