Skip to main content
Springer Nature Link
Log in

Fast Algorithms for Solving RFMrLrR Circulant Linear Systems in Communication

  • Conference paper
Information Computing and Applications (ICICA 2013)

Part of the book series: Communications in Computer and Information Science ((CCIS,volume 391))

Included in the following conference series:

  • 1591 Accesses

Abstract

In this paper, fast algorithms for solving RFMrLrR circulant linear systems are presented by the fast algorithm for computing polynomials. The extended algorithms are used to solve the RLMrFrL circulant linear systems. Examples show the effectiveness of the algorithms.

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

Access this chapter

Log in via an institution

Subscribe and save

Springer+ Basic
$34.99 /Month
  • Get 10 units per month
  • Download Article/Chapter or eBook
  • 1 Unit = 1 Article or 1 Chapter
  • Cancel anytime
Subscribe now

Buy Now

Chapter
USD 29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever

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.

Similar content being viewed by others

References

  1. Williams, F.J.M., Sloane, N.J.A.: The Theory Error-correcting Codes. North-Holland, Amsterdam (1981)

    Google Scholar 

  2. David, C.: Regular Representations of Semisimple Algebras, Separable Field Extensions, Group Characters, Generalized Circulants, and Generalized Cyclic Codes. Linear Algebra Appl. 218, 147–183 (1995)

    Article  MathSciNet  MATH  Google Scholar 

  3. He, C.Y.: On the Fast Solution of r-circulant Linear Systems. Syst. Syst. Sci. Math. 21(2), 182–189 (2001) (in Chinese)

    Google Scholar 

  4. Cline, R.E., Plemmons, R.J., Worm, G.: Generalized Inverses of Toeplitz Matrix. Linear Algebra Appl. 8, 25–33 (1974)

    Article  MathSciNet  MATH  Google Scholar 

  5. Chen, M.K.: On the Solution of Circulant Linear System. SIAM J. Numer. Anal. 24(3), 668–683 (1987)

    Article  MathSciNet  MATH  Google Scholar 

  6. Jiang, Z.L., Xu, Z.B.: A New Algorithm for Computing the Inverse and Generalized Inverse of the Scaled Factor Circulant Matrix. J. Computa. Math. 26, 112–122 (2008)

    MathSciNet  MATH  Google Scholar 

  7. Jiang, Z.L., Xu, Z.B.: Efficient Algorithm for Finding the Inverse and Group Inverse of FLS r-circulant Matrix. J. Appl. Math. Comput. 18, 45–57 (2005)

    Article  MathSciNet  MATH  Google Scholar 

  8. Jiang, Z.L.: Fast Algorithms for Solving FLS r-circulant Linear Systems. In: SCET 2012 (Xi’an), pp. 141–144 (2012)

    Google Scholar 

  9. Jiang, Z., Lu, F.: The Sum and Product of Jacobsthal and Jacobsthal-Lucas Numbers Representation by Matrix Method. Ars Combinatoria, 110 (July 2013)

    Google Scholar 

  10. Shen, N., Jiang, Z., Li, J.: On Explicit Determinants of the RFMLR and RLMFL Circulant Matrices Involving Certain Famous Numbers. WSEAS Transactions on Mathematics 12(1), 42–53 (2013)

    Google Scholar 

  11. Jiang, Z.: Efficient Algorithms for Finding the Minimal Polynomials and the Inverses of Level-k FLS-circulant Matrices. WSEAS Transactions on Mathematics (to appear, 2013)

    Google Scholar 

  12. Li, J., Jiang, Z., Shen, N.: Explicit Determinants of the Fibonacci RFPL Circulant and Lucas RFPL Circulant Matrix. JP Journal of Algebra, Number Theory and Applications 28(2), 167–179 (2013)

    MathSciNet  MATH  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Department of Mathematics, Linyi University, Linyi, 276005, P.R. China

    Zhao-Lin Jiang & Ru-Li Chen

Authors
  1. Zhao-Lin Jiang
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Ru-Li Chen
    View author publications

    You can also search for this author in PubMed Google Scholar

Editor information

Editors and Affiliations

  1. Shanghai Jiao Tong University, 800 Dongchuan Road, Dianxinqunlou 1-401, 200240, Shanghai, China

    Yuhang Yang

  2. School of Electrical and Electronic Engineering, Nanyang Technological University, Nanyang Avenue, 639798, Singapore, Singapore

    Maode Ma

  3. College of Science, Hebei United University, 063009, Tangshan, Hebei, China

    Baoxiang Liu

Rights and permissions

Reprints and permissions

Copyright information

© 2013 Springer-Verlag Berlin Heidelberg

About this paper

Cite this paper

Jiang, ZL., Chen, RL. (2013). Fast Algorithms for Solving RFMrLrR Circulant Linear Systems in Communication. In: Yang, Y., Ma, M., Liu, B. (eds) Information Computing and Applications. ICICA 2013. Communications in Computer and Information Science, vol 391. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-53932-9_6

Download citation

  • DOI: https://doi.org/10.1007/978-3-642-53932-9_6

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-642-53931-2

  • Online ISBN: 978-3-642-53932-9

  • eBook Packages: Computer ScienceComputer Science (R0)

Publish with us

Policies and ethics