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Spectra of Discrete Multi-Splitting Waveform Relaxation Methods to Determining Periodic Solutions of Linear Differential-Algebraic Equations

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Computer, Informatics, Cybernetics and Applications

Part of the book series: Lecture Notes in Electrical Engineering ((LNEE,volume 107))

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Abstract

This chapter proposed spectra of discrete multi-splitting waveform relaxation (DMSWR) method to determine the periodic solutions of linear differential-algebraic equations. Based on the spectral radius of the derived operator by decoupled process, we obtained some convergent conditions for DMSWR method. The DMSWR method is an acceleration technique of the periodic waveform relaxation. A numerical example in circuit simulation is provided to further confirm the theoretical analysis and also to show that the multi-splitting technique can effectively accelerate the convergent performance of the iterative process.

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Acknowledgments

This work was supported by the Ph.D. Programs Foundation of Shaanxi University of Science and Technology (Grant No. BJ10-23).

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Authors and Affiliations

  1. Faculty of Science, Shaanxi University of Science and Technology, Xi’an, 710021, People’s Republic of China

    Xiaolin Lin, Liming Liu & Yuan Sang

  2. College of Electric and Information Engineering, Shaanxi University of Science and Technology, Xi’an, 710021, People’s Republic of China

    Liming Liu, Yuan Sang & Yumei Wang

  3. Manage Center of Internet, Shaanxi University of Science and Technology, Xi’an, 710021, People’s Republic of China

    Hong Wei

  4. Center of Computer Teach and Experiment, Wuyi University, Wuyishan, 354300, People’s Republic of China

    Ronghui Lu

Authors
  1. Xiaolin Lin
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  2. Liming Liu
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  3. Hong Wei
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  4. Yuan Sang
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  5. Yumei Wang
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  6. Ronghui Lu
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Corresponding author

Correspondence to Xiaolin Lin .

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Editors and Affiliations

  1. Chinese Academy of Engineering, Beijing, China, People's Republic

    Xingui He

  2. Zhejiang Gongshang University, Beijing, China, People's Republic

    Ertian Hua

  3. Zhejiang Gongshang University, Hangzhou, China, People's Republic

    Yun Lin

  4. , School of Automation, Wuhan University of Technology, East District of Wuhan University, Luoshi Road 122, Wuhan, 4300, China, People's Republic

    Xiaozhu Liu

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© 2012 Springer Science+Business Media B.V.

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Lin, X., Liu, L., Wei, H., Sang, Y., Wang, Y., Lu, R. (2012). Spectra of Discrete Multi-Splitting Waveform Relaxation Methods to Determining Periodic Solutions of Linear Differential-Algebraic Equations. In: He, X., Hua, E., Lin, Y., Liu, X. (eds) Computer, Informatics, Cybernetics and Applications. Lecture Notes in Electrical Engineering, vol 107. Springer, Dordrecht. https://doi.org/10.1007/978-94-007-1839-5_10

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  • DOI: https://doi.org/10.1007/978-94-007-1839-5_10

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  • Publisher Name: Springer, Dordrecht

  • Print ISBN: 978-94-007-1838-8

  • Online ISBN: 978-94-007-1839-5

  • eBook Packages: EngineeringEngineering (R0)

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