PARAMETRIC SMITH ITERATIVE ALGORITHMS FOR DISCRETE LYAPUNOV MATRIX EQUATIONS

Ai Guo Wu; YING ZHANG; HUI JIE SUN

doi:10.3934/jimo.2019093

PARAMETRIC SMITH ITERATIVE ALGORITHMS FOR DISCRETE LYAPUNOV MATRIX EQUATIONS

Ai Guo Wu
, YING ZHANG^*
, HUI JIE SUN

^*Corresponding author for this work

Harbin Institute of Technology Shenzhen

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

3 Scopus citations

Abstract

An iterative algorithm is established in this paper for solving the discrete Lyapunov matrix equations. The proposed algorithm contains a tunable parameter, and includes the Smith iteration as a special case, and thus is called the parametric Smith iterative algorithm. Some convergence conditions are developed for the proposed parametric Smith iterative algorithm. Moreover, the optimal parameter for the proposed algorithm to have the fastest convergence rate is also provided for a special case. Finally, numerical examples are employed to illustrate the effectiveness of the proposed algorithm.

Original language	English
Pages (from-to)	3047-3063
Number of pages	17
Journal	Journal of Industrial and Management Optimization
Volume	16
Issue number	6
DOIs	https://doi.org/10.3934/jimo.2019093
State	Published - Nov 2020
Externally published	Yes

Keywords

and phrases. Lyapunov matrix equations
convergence rate
iterative algorithms

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10.3934/jimo.2019093

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title = "PARAMETRIC SMITH ITERATIVE ALGORITHMS FOR DISCRETE LYAPUNOV MATRIX EQUATIONS",

abstract = "An iterative algorithm is established in this paper for solving the discrete Lyapunov matrix equations. The proposed algorithm contains a tunable parameter, and includes the Smith iteration as a special case, and thus is called the parametric Smith iterative algorithm. Some convergence conditions are developed for the proposed parametric Smith iterative algorithm. Moreover, the optimal parameter for the proposed algorithm to have the fastest convergence rate is also provided for a special case. Finally, numerical examples are employed to illustrate the effectiveness of the proposed algorithm.",

keywords = "and phrases. Lyapunov matrix equations, convergence rate, iterative algorithms",

author = "Wu, \{Ai Guo\} and YING ZHANG and SUN, \{HUI JIE\}",

year = "2020",

month = nov,

doi = "10.3934/jimo.2019093",

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PY - 2020/11

Y1 - 2020/11

N2 - An iterative algorithm is established in this paper for solving the discrete Lyapunov matrix equations. The proposed algorithm contains a tunable parameter, and includes the Smith iteration as a special case, and thus is called the parametric Smith iterative algorithm. Some convergence conditions are developed for the proposed parametric Smith iterative algorithm. Moreover, the optimal parameter for the proposed algorithm to have the fastest convergence rate is also provided for a special case. Finally, numerical examples are employed to illustrate the effectiveness of the proposed algorithm.

AB - An iterative algorithm is established in this paper for solving the discrete Lyapunov matrix equations. The proposed algorithm contains a tunable parameter, and includes the Smith iteration as a special case, and thus is called the parametric Smith iterative algorithm. Some convergence conditions are developed for the proposed parametric Smith iterative algorithm. Moreover, the optimal parameter for the proposed algorithm to have the fastest convergence rate is also provided for a special case. Finally, numerical examples are employed to illustrate the effectiveness of the proposed algorithm.

KW - and phrases. Lyapunov matrix equations

KW - convergence rate

KW - iterative algorithms

UR - https://www.scopus.com/pages/publications/85096244613

U2 - 10.3934/jimo.2019093

DO - 10.3934/jimo.2019093

M3 - 文章

AN - SCOPUS:85096244613

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JO - Journal of Industrial and Management Optimization

JF - Journal of Industrial and Management Optimization

IS - 6

ER -

PARAMETRIC SMITH ITERATIVE ALGORITHMS FOR DISCRETE LYAPUNOV MATRIX EQUATIONS

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Keywords

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