The asymptotic analysis of the structure-preserving doubling algorithms

Yueh Cheng Kuo; Wen Wei Lin; Shih Feng Shieh

doi:10.1016/j.laa.2017.06.005

The asymptotic analysis of the structure-preserving doubling algorithms

Yueh Cheng Kuo, Wen Wei Lin, Shih Feng Shieh^*

^*此作品的通信作者

數學系

研究成果: 雜誌貢獻 › 期刊論文 › 同行評審

3 引文斯高帕斯（Scopus）

摘要

This paper is the second part of [15]. Taking advantage of the special structure and properties of the Hamiltonian matrix, we apply a symplectically similar transformation introduced by [18] to reduce H to a Hamiltonian Jordan canonical form J. The asymptotic analysis of the structure-preserving flows and RDEs is studied by using e^Jt. The convergence of the SDA as well as its rate can thus result from the study of the structure-preserving flows. A complete asymptotic dynamics of the SDA is investigated, including the linear and quadratic convergence studied in the literature [3,12,13].

原文	英語
頁（從 - 到）	318-355
頁數	38
期刊	Linear Algebra and Its Applications
卷	531
DOIs	https://doi.org/10.1016/j.laa.2017.06.005
出版狀態	已發佈 - 2017 10月 15

ASJC Scopus subject areas

代數與數理論
數值分析
幾何和拓撲
離散數學和組合

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10.1016/j.laa.2017.06.005

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title = "The asymptotic analysis of the structure-preserving doubling algorithms",

abstract = "This paper is the second part of [15]. Taking advantage of the special structure and properties of the Hamiltonian matrix, we apply a symplectically similar transformation introduced by [18] to reduce H to a Hamiltonian Jordan canonical form J. The asymptotic analysis of the structure-preserving flows and RDEs is studied by using eJt. The convergence of the SDA as well as its rate can thus result from the study of the structure-preserving flows. A complete asymptotic dynamics of the SDA is investigated, including the linear and quadratic convergence studied in the literature [3,12,13].",

keywords = "Convergence rates, Matrix Riccati differential equations, Matrix equations, Structure-preserving doubling algorithms, Structure-preserving flows, Symplectic pairs",

author = "Kuo, {Yueh Cheng} and Lin, {Wen Wei} and Shieh, {Shih Feng}",

note = "Publisher Copyright: {\textcopyright} 2017 Elsevier Inc.",

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day = "15",

doi = "10.1016/j.laa.2017.06.005",

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AU - Kuo, Yueh Cheng

AU - Lin, Wen Wei

AU - Shieh, Shih Feng

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Y1 - 2017/10/15

N2 - This paper is the second part of [15]. Taking advantage of the special structure and properties of the Hamiltonian matrix, we apply a symplectically similar transformation introduced by [18] to reduce H to a Hamiltonian Jordan canonical form J. The asymptotic analysis of the structure-preserving flows and RDEs is studied by using eJt. The convergence of the SDA as well as its rate can thus result from the study of the structure-preserving flows. A complete asymptotic dynamics of the SDA is investigated, including the linear and quadratic convergence studied in the literature [3,12,13].

AB - This paper is the second part of [15]. Taking advantage of the special structure and properties of the Hamiltonian matrix, we apply a symplectically similar transformation introduced by [18] to reduce H to a Hamiltonian Jordan canonical form J. The asymptotic analysis of the structure-preserving flows and RDEs is studied by using eJt. The convergence of the SDA as well as its rate can thus result from the study of the structure-preserving flows. A complete asymptotic dynamics of the SDA is investigated, including the linear and quadratic convergence studied in the literature [3,12,13].

KW - Convergence rates

KW - Matrix Riccati differential equations

KW - Matrix equations

KW - Structure-preserving doubling algorithms

KW - Structure-preserving flows

KW - Symplectic pairs

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DO - 10.1016/j.laa.2017.06.005

M3 - Article

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SP - 318

EP - 355

JO - Linear Algebra and Its Applications

JF - Linear Algebra and Its Applications

ER -

The asymptotic analysis of the structure-preserving doubling algorithms

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