Skip to main content
SpringerLink
Log in

Levinson-Durbin algorithm as a Szegö polynomial recursion

  • Published:
Computational Statistics Aims and scope Submit manuscript

Summary

In this paper it is shown that the famous Levinson-Durbin algorithm is just a recursive algorithm presented previously by Szegö.

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

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Similar content being viewed by others

References

  • Anderson, T. W. (1971), The Statistical Analysis of Time Series, Wiley, New York.

    MATH  Google Scholar 

  • Choi, B.S. (1992), ARMA Model Identification, Springer-Verlag, New York.

    Book  Google Scholar 

  • Choi, B.S. (1997), ‘A recursive algorithm for solving the spatial Yule-Walker equations of causal spatial AR models’, Statistics and Probability Letters 33, 241–251.

    Article  MathSciNet  Google Scholar 

  • Durbin, J. (1960), ‘The fitting of time series models’, Inter. Statistical Review 28, 233–244.

    Article  Google Scholar 

  • Grenander, U. and Szegö, G. (1955), Toeplitz Forms and Their Applications, Chelsea Pub. Co., New York.

    MATH  Google Scholar 

  • Haykin, S. (1996), Adaptive Filter Theory, 3rd edn., Prentice-Hall, New Jersey.

    MATH  Google Scholar 

  • Justice, J.H. (1977), ‘A Levinson-type algorithm for two-dimensional Wiener filtering using bivariate Szegö polynomials’, Proc. IEEE 65, 882–886.

    Article  Google Scholar 

  • Levinson, N. (1947),‘The Wiener RMS (Root Mean Square) error criterion in filter design and prediction’, J. Mathematics and Physics 25, 261–278.

    Article  MathSciNet  Google Scholar 

  • Szegö, G. (1921), ‘Beiträge zur Theorie der Toeplitzschen Formen II’, Mathematische Zeitschrift 9, 167–190.

    Article  MathSciNet  Google Scholar 

  • Szegö, G. (1939), Orthogonal Polynomials, American Mathematical Society, New York.

    MATH  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Division of Mathematical Sciences, Pukyong National University, Pusan, Korea

    Seongbaek Yi

  2. Department of Applied Statistics, Yonsei University, Seoul, Korea

    ByoungSeon Choi

Authors
  1. Seongbaek Yi
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. ByoungSeon Choi
    View author publications

    You can also search for this author in PubMed Google Scholar

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Yi, S., Choi, B. Levinson-Durbin algorithm as a Szegö polynomial recursion. Computational Statistics 17, 59–64 (2002). https://doi.org/10.1007/s001800200090

Download citation

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s001800200090

Keywords

Search

Navigation