The asymptotic analysis of the structure-preserving doubling algorithms

Yueh Cheng Kuo, Wen Wei Lin, Shih Feng Shieh

Research output: Contribution to journalArticle

1 Citation (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 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].

Original languageEnglish
Pages (from-to)318-355
Number of pages38
JournalLinear Algebra and Its Applications
Volume531
DOIs
Publication statusPublished - 2017 Oct 15

Fingerprint

Hamiltonians
Asymptotic analysis
Flow structure
Doubling
Asymptotic Analysis
Jordan Canonical Form
Hamiltonian Matrix
Linear Convergence
Quadratic Convergence

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

Cite this

The asymptotic analysis of the structure-preserving doubling algorithms. / Kuo, Yueh Cheng; Lin, Wen Wei; Shieh, Shih Feng.

In: Linear Algebra and Its Applications, Vol. 531, 15.10.2017, p. 318-355.

Research output: Contribution to journalArticle

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