Skip to main content
SpringerLink
Log in

A New Computational Algorithm for Solving Periodic Sevendiagonal Linear Systems

  • Conference paper
Artificial Intelligence and Computational Intelligence (AICI 2010)

Part of the book series: Lecture Notes in Computer Science ((LNAI,volume 6320))

  • 1467 Accesses

Abstract

Many issues in engineering computation and practical application that ultimately boil down to a matrix computation. And different applications will lead to some of the special sparse structure of the matrix computation. A modified chasing method has been proposed to solve the sevendiagonal linear equations in this paper firstly. By using this method, the condition that each principal minor sequence of coefficient matrix must nonzero is unnecessary. At the same time, we present a new computational algorithm for solving periodic sevendiagonal linear systems. An example is given in order to illustrate the algorithm.

This is a preview of subscription content, log in via an institution to check access.

Access this chapter

Log in via an institution
Chapter
USD 29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD 39.99
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD 54.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Institutional subscriptions

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. Allen III, M.B., Isaacson, E.L.: Numerical Analysis for Applied Science. Wiley-Interscience, John Wiley & Sons (1997)

    Google Scholar 

  2. Chen, M.: On the solution of circulant linear systems. SIAM J. Numer. Anal. 24, 668–683 (1987)

    Article  MathSciNet  MATH  Google Scholar 

  3. Rao, S.S.: Applied Numerical Methods for Engineers and Scientists, Upper Saddle River, New Jersey (2002)

    Google Scholar 

  4. Batista, M.: A cyclic block-tridiagonal solver. Adv. Eng. Software 37(2), 69–74 (2006)

    Article  Google Scholar 

  5. Wei, Y.M., Diao, H.A.: On group of singular Toeplitz matrices. Linear Algebra Appl. 399, 109–123 (2005)

    Article  MathSciNet  MATH  Google Scholar 

  6. Chawla, M., Khazal, R.R.: A parallel elimination method for periodic tri-diagonal systems. Int. J. Comput. Math. 79(4), 473–484 (2002)

    Article  MATH  Google Scholar 

  7. Karawia, A.A.: A computational algorithm for solving periodic pentadiagonal linear systems. Appl. Math. Comput. 174, 613–618 (2006)

    MathSciNet  MATH  Google Scholar 

  8. Zhao, X.L., Huang, T.Z.: On the inverse of a general pentadiagonal matrix. Appl. Math. Comput. 202, 639–646 (2008)

    MathSciNet  MATH  Google Scholar 

  9. El-Mikkawy, M.E.A., Rahmo, E.D.: A new recursive algorithm for inverting general periodic pentadiagonal and anti-pentadiagonal matrices. Appl. Math. Comput. 207, 164–170 (2009)

    MathSciNet  MATH  Google Scholar 

  10. El-Mikkawy, M.E.A.: A new computational algorithm for solving periodic tri-diagonal linear systems. Appl. Math. Comput. 161, 691–696 (2005)

    MathSciNet  MATH  Google Scholar 

  11. Lin, X.L., Jiang, Y.L.: QR decomposition and algorithm for unitary symmetric matrix. Chinese Journal of Computers 28, 817–822 (2005)

    MathSciNet  Google Scholar 

  12. Lin, X.L., Jiang, Y.L.: Numerical algorithm for constructing Lyapunov functions of polynomial diffrential system. Appl. Math. Comput. 1-2, 247–262 (2009)

    MATH  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Faculty of Science, Shaanxi University of Science & Technology, Xi’an, 710021, P.R. China

    Xiao-Lin Lin & Ji-Teng Jia

Authors
  1. Xiao-Lin Lin
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Ji-Teng Jia
    View author publications

    You can also search for this author in PubMed Google Scholar

Editor information

Editors and Affiliations

  1. Department of Business Administration, Caritas Francis Hsu College, 18 Chui Ling Road, Tseung Kwan O, Hong Kong, China

    Fu Lee Wang

  2. School of Business Information Technology, RMIT University, City Campus, 124 La Trobe Street, 3000, Melbourne, Victoria, Australia

    Hepu Deng

  3. Department of Computer Science, Nanjing University, 210093, Nanjing, China

    Yang Gao

  4. School of Computer, Nanjing University of Posts and Telecommunications, 210003, Nanjing, China

    Jingsheng Lei

Rights and permissions

Reprints and permissions

Copyright information

© 2010 Springer-Verlag Berlin Heidelberg

About this paper

Cite this paper

Lin, XL., Jia, JT. (2010). A New Computational Algorithm for Solving Periodic Sevendiagonal Linear Systems. In: Wang, F.L., Deng, H., Gao, Y., Lei, J. (eds) Artificial Intelligence and Computational Intelligence. AICI 2010. Lecture Notes in Computer Science(), vol 6320. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-16527-6_26

Download citation

  • DOI: https://doi.org/10.1007/978-3-642-16527-6_26

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-642-16526-9

  • Online ISBN: 978-3-642-16527-6

  • eBook Packages: Computer ScienceComputer Science (R0)

Publish with us

Policies and ethics

Search

Navigation