A modified Krylov subspace model reduction method based on the Chebyshev polynomials

Xiaolong Wang; Haibao Chen; Yaolin Jiang

doi:10.1109/MACE.2011.5988692

A modified Krylov subspace model reduction method based on the Chebyshev polynomials

Xiaolong Wang
, Haibao Chen
, Yaolin Jiang

School of Mathematics and Statistics

Xi'an Jiaotong University

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution › peer-review

3 Scopus citations

Abstract

In this paper, we present a modified Krylov subspace model reduction method for linear time invariable systems based on the Chebyshev polynomials. Noting the structure of the Chebyshev polynomial coefficient matrices, which are calculated approximately via the Chebyshev polynomial expansion of the state variable, we employ Krylov subspace to construct decent projection matrices. A reduced order system is produced in two-sided projection framework by combining the time and the frequency domain analysis. Two numerical examples are used to illustrate the efficiency of the method.

Original language	English
Title of host publication	2011 2nd International Conference on Mechanic Automation and Control Engineering, MACE 2011 - Proceedings
Pages	7123-7126
Number of pages	4
DOIs	https://doi.org/10.1109/MACE.2011.5988692
State	Published - 2011
Event	2011 2nd International Conference on Mechanic Automation and Control Engineering, MACE 2011 - Inner Mongolia, China Duration: 15 Jul 2011 → 17 Jul 2011

Publication series

Name	2011 2nd International Conference on Mechanic Automation and Control Engineering, MACE 2011 - Proceedings

Conference

Conference	2011 2nd International Conference on Mechanic Automation and Control Engineering, MACE 2011
Country/Territory	China
City	Inner Mongolia
Period	15/07/11 → 17/07/11

Keywords

Krylov subspace
Linear time invariable systems
Model reduction
The Chebyshev polynomials

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10.1109/MACE.2011.5988692

Cite this

Wang, X., Chen, H., & Jiang, Y. (2011). A modified Krylov subspace model reduction method based on the Chebyshev polynomials. In 2011 2nd International Conference on Mechanic Automation and Control Engineering, MACE 2011 - Proceedings (pp. 7123-7126). Article 5988692 (2011 2nd International Conference on Mechanic Automation and Control Engineering, MACE 2011 - Proceedings). https://doi.org/10.1109/MACE.2011.5988692

Wang, Xiaolong ; Chen, Haibao ; Jiang, Yaolin. / A modified Krylov subspace model reduction method based on the Chebyshev polynomials. 2011 2nd International Conference on Mechanic Automation and Control Engineering, MACE 2011 - Proceedings. 2011. pp. 7123-7126 (2011 2nd International Conference on Mechanic Automation and Control Engineering, MACE 2011 - Proceedings).

@inproceedings{40370ec9dd07446081767d33a3df9ed3,

title = "A modified Krylov subspace model reduction method based on the Chebyshev polynomials",

abstract = "In this paper, we present a modified Krylov subspace model reduction method for linear time invariable systems based on the Chebyshev polynomials. Noting the structure of the Chebyshev polynomial coefficient matrices, which are calculated approximately via the Chebyshev polynomial expansion of the state variable, we employ Krylov subspace to construct decent projection matrices. A reduced order system is produced in two-sided projection framework by combining the time and the frequency domain analysis. Two numerical examples are used to illustrate the efficiency of the method.",

keywords = "Krylov subspace, Linear time invariable systems, Model reduction, The Chebyshev polynomials",

author = "Xiaolong Wang and Haibao Chen and Yaolin Jiang",

year = "2011",

doi = "10.1109/MACE.2011.5988692",

language = "英语",

isbn = "9781424494392",

series = "2011 2nd International Conference on Mechanic Automation and Control Engineering, MACE 2011 - Proceedings",

pages = "7123--7126",

booktitle = "2011 2nd International Conference on Mechanic Automation and Control Engineering, MACE 2011 - Proceedings",

note = "2011 2nd International Conference on Mechanic Automation and Control Engineering, MACE 2011 ; Conference date: 15-07-2011 Through 17-07-2011",

}

Wang, X, Chen, H & Jiang, Y 2011, A modified Krylov subspace model reduction method based on the Chebyshev polynomials. in 2011 2nd International Conference on Mechanic Automation and Control Engineering, MACE 2011 - Proceedings., 5988692, 2011 2nd International Conference on Mechanic Automation and Control Engineering, MACE 2011 - Proceedings, pp. 7123-7126, 2011 2nd International Conference on Mechanic Automation and Control Engineering, MACE 2011, Inner Mongolia, China, 15/07/11. https://doi.org/10.1109/MACE.2011.5988692

A modified Krylov subspace model reduction method based on the Chebyshev polynomials. / Wang, Xiaolong; Chen, Haibao; Jiang, Yaolin.
2011 2nd International Conference on Mechanic Automation and Control Engineering, MACE 2011 - Proceedings. 2011. p. 7123-7126 5988692 (2011 2nd International Conference on Mechanic Automation and Control Engineering, MACE 2011 - Proceedings).

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution › peer-review

TY - GEN

T1 - A modified Krylov subspace model reduction method based on the Chebyshev polynomials

AU - Wang, Xiaolong

AU - Chen, Haibao

AU - Jiang, Yaolin

PY - 2011

Y1 - 2011

N2 - In this paper, we present a modified Krylov subspace model reduction method for linear time invariable systems based on the Chebyshev polynomials. Noting the structure of the Chebyshev polynomial coefficient matrices, which are calculated approximately via the Chebyshev polynomial expansion of the state variable, we employ Krylov subspace to construct decent projection matrices. A reduced order system is produced in two-sided projection framework by combining the time and the frequency domain analysis. Two numerical examples are used to illustrate the efficiency of the method.

AB - In this paper, we present a modified Krylov subspace model reduction method for linear time invariable systems based on the Chebyshev polynomials. Noting the structure of the Chebyshev polynomial coefficient matrices, which are calculated approximately via the Chebyshev polynomial expansion of the state variable, we employ Krylov subspace to construct decent projection matrices. A reduced order system is produced in two-sided projection framework by combining the time and the frequency domain analysis. Two numerical examples are used to illustrate the efficiency of the method.

KW - Krylov subspace

KW - Linear time invariable systems

KW - Model reduction

KW - The Chebyshev polynomials

UR - https://www.scopus.com/pages/publications/80054812428

U2 - 10.1109/MACE.2011.5988692

DO - 10.1109/MACE.2011.5988692

M3 - 会议稿件

AN - SCOPUS:80054812428

SN - 9781424494392

T3 - 2011 2nd International Conference on Mechanic Automation and Control Engineering, MACE 2011 - Proceedings

SP - 7123

EP - 7126

BT - 2011 2nd International Conference on Mechanic Automation and Control Engineering, MACE 2011 - Proceedings

T2 - 2011 2nd International Conference on Mechanic Automation and Control Engineering, MACE 2011

Y2 - 15 July 2011 through 17 July 2011

ER -

Wang X, Chen H, Jiang Y. A modified Krylov subspace model reduction method based on the Chebyshev polynomials. In 2011 2nd International Conference on Mechanic Automation and Control Engineering, MACE 2011 - Proceedings. 2011. p. 7123-7126. 5988692. (2011 2nd International Conference on Mechanic Automation and Control Engineering, MACE 2011 - Proceedings). doi: 10.1109/MACE.2011.5988692

A modified Krylov subspace model reduction method based on the Chebyshev polynomials

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