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^*

^*Corresponding author for this work

Department of Mathematics

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

2 Citations (Scopus)

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 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].

Original language	English
Pages (from-to)	318-355
Number of pages	38
Journal	Linear Algebra and Its Applications
Volume	531
DOIs	https://doi.org/10.1016/j.laa.2017.06.005
Publication status	Published - 2017 Oct 15

Keywords

Convergence rates
Matrix Riccati differential equations
Matrix equations
Structure-preserving doubling algorithms
Structure-preserving flows
Symplectic pairs

ASJC Scopus subject areas

Algebra and Number Theory
Numerical Analysis
Geometry and Topology
Discrete Mathematics and Combinatorics

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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",

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T1 - The asymptotic analysis of the structure-preserving doubling algorithms

AU - Kuo, Yueh Cheng

AU - Lin, Wen Wei

AU - Shieh, Shih Feng

PY - 2017/10/15

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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VL - 531

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

Abstract

Keywords

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