Location via proxy:   [ UP ]  
[Report a bug]   [Manage cookies]                
Skip to main content
SpringerLink
Log in

An Adaptive Algorithm Finding Multiple Roots of Polynomials

  • Conference paper
Advances in Neural Networks - ISNN 2008 (ISNN 2008)

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 5264))

Included in the following conference series:

Abstract

An adaptive algorithm is proposed to find multiple roots of polynomials which were not well solved by the other methods. Its convergence was presented and proved. The computation is carried out by simple steepest descent rule with adaptive variable learning rate. The specific examples showed that the proposed method can find the multiple roots of polynomials at a very rapid convergence and very high accuracy with less computation.

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 129.00
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. Burden, R.L., Faires, J.D.: Numerical Analysis, 7th edn., pp. 47–103. Thomson Learning, Inc. (August 2001)

    Google Scholar 

  2. Zeng, Z.Z., Wen, H.: Numerical Computation, 1st edn., pp. 88–108. Qinghua University Press, Beijing (2005)

    Google Scholar 

  3. Xu, C.-F., Wang, M.M., Wang, N.H.: An Accelerated Iiteration Solution to Nonlinear Equation in Large Scope. J. Huazhong Univ. of Sci. & Tech(Nature Science Edition) 4, 122–124 (2006)

    Google Scholar 

  4. Markus, L., Frenzel, B.-C.: Polynomial Root Finding. IEEE Signal Processing Letters 10, 141–143 (1994)

    Google Scholar 

  5. Jenkins, M.A., Traub, J.F.: A Three-Stage Algorithm for Real Polynomials Using Quadratic Iiteration. SIAM Journal On Numerical Analysis 4, 545–566 (1970)

    Article  MathSciNet  Google Scholar 

  6. Orchard, H.J.: The Laguerre Method for Finding the Zeros of Polynomials. IEEE Trans. On Circuits and Systems 11, 1377–1381 (1989)

    Article  MathSciNet  Google Scholar 

  7. Lucas, T.N.: Finding Roots of Polynomials by Using the Routh Array. IEEE Electronics Letters 16, 1519–1521 (1996)

    Article  Google Scholar 

  8. Truong, T.K., Jeng, J.H., Reed, I.S.: Fast Algorithm for Computing the Roots of Error Locator Polynomials up to Degree 11 in Reed-Solomon Decoders. IEEE Trans. Commun. 49, 779–783 (2001)

    Article  MATH  Google Scholar 

  9. Sergei, V.F., Peter, V.T.: Finding Roots of Polynomials over Finite Fields. IEEE Trans. Commun. 50, 1709–1711 (2002)

    Article  Google Scholar 

  10. Cui, X.-Z., Yang, D.-D., Long, Y.: The Fast Halley Algorithm for Finding All Zeros of a Polynomial. Chinese Journal of Engineering Mathematics 23, 511–517 (2006)

    MATH  MathSciNet  Google Scholar 

  11. Ehrlich, L.W.: A Modified Newton Method for Polynomials. Comm. ACM 10, 107–108 (1967)

    Article  MATH  Google Scholar 

  12. Huang, Q.-L.: An Improvement on a Modified Newton Method. Numerical Mathematics: A Journal of Chinese Universities 11, 313–319 (2002)

    Google Scholar 

  13. Huang, Q.-L., Wu, J.C.: On a Modified Newton Method for Simultaneous Finding Polynomial Zeros. Journal On Numerical Methods And Computer Applications (Beijing, China) 28, 292–298 (2006)

    MathSciNet  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. College of Electrical & Information Engineering, Changsha University of Science &Technology, Changsha, Hunan, 410076, China

    Wei Zhu, Zhe-zhao Zeng & Dong-mei Lin

  2. College of Electrical & Information Engineering, Hunan University, Changsha, Hunan, 410082, China

    Wei Zhu

Authors
  1. Wei Zhu
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Zhe-zhao Zeng
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Dong-mei Lin
    View author publications

    You can also search for this author in PubMed Google Scholar

Editor information

Editors and Affiliations

  1. Department of Computer Science and Technology, Tsinghu University, 100084, Beijing, China

    Fuchun Sun

  2. Institute TAMS (Technical Aspects of Multimodal Systems), department of Informatics, University of Hamburg, Vogt-Koelln-Straße 30, 22527, Hamburg, Germany

    Jianwei Zhang

  3. Intel China Research Center, 8/F, Peking University, Department of Machine Intelligence, 100871, Beijing, China

    Ying Tan

  4. Department of Mathematics, Southeast University, 210096, Nanjing, China

    Jinde Cao

  5. Departamento de Control Automático, CINVESTAV-IPN, A.P. 14-740, Av.IPN 2508, 07360, México D.F., México

    Wen Yu

Rights and permissions

Reprints and permissions

Copyright information

© 2008 Springer-Verlag Berlin Heidelberg

About this paper

Cite this paper

Zhu, W., Zeng, Zz., Lin, Dm. (2008). An Adaptive Algorithm Finding Multiple Roots of Polynomials. In: Sun, F., Zhang, J., Tan, Y., Cao, J., Yu, W. (eds) Advances in Neural Networks - ISNN 2008. ISNN 2008. Lecture Notes in Computer Science, vol 5264. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-87734-9_77

Download citation

  • DOI: https://doi.org/10.1007/978-3-540-87734-9_77

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-87733-2

  • Online ISBN: 978-3-540-87734-9

  • eBook Packages: Computer ScienceComputer Science (R0)

Publish with us

Policies and ethics

Search

Navigation