Skip to main content
SpringerLink
Log in

Zeros of a rational function defined by its Laurent expansion

  • Conference paper
  • First Online:
Padé Approximation and its Applications Bad Honnef 1983

Part of the book series: Lecture Notes in Mathematics ((LNM,volume 1071))

Abstract

If a rational function is defined by a Laurent series in an annular region, then we can construct a qd-table from its Laurent coefficients. The limits of certain rows and columns in this table give you information about the pole/zero structure of the rational function. This property was known for the column-pole connection [11] but is not for its row-zero connection.

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 34.99
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD 46.00
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. A. Bultheel, P. Dewilde (1980) On the relation between Padé approximation and Levinson/Schur recursive methods. In signal processing: theories and applications, M. Kunt, F. de Coulon (eds.), North Holland, P. 517–523.

    Google Scholar 

  2. A. Bultheel (1979) Recursive algorithms for the Padé table: two approaches in Padé approximation and its application, Lecture Notes in Mathematics 765, Springer Verlag, p. 211–230.

    Google Scholar 

  3. A. Bultheel (1982) Epsilon and qd algorithms for the matrix Padé and 2-D Padé problem. Report TW 57, K.U.Leuven, May 1982.

    Google Scholar 

  4. W.B. Gragg (1972) The Padé table and its relation to certain algorithms of numerical analysis. Siam Review 14 (1), 1–62.

    Article  MathSciNet  MATH  Google Scholar 

  5. G.A. Baker Jr, P. Graves-Morris (1981) Padé approximats: basic theory, Addison-Wesley, Reading, Mass.

    MATH  Google Scholar 

  6. W.B. Jones, W.J. Thron (1980) Continued fractions, analytic theory and applications. Addison-Wesley, Reading, Mass.

    MATH  Google Scholar 

  7. J.H. McCabe, J.A. Murphy (1976) Continued fractions which correspond to power series at two points. J. Inst. Math. Appl. 17, 233–247.

    Article  MathSciNet  MATH  Google Scholar 

  8. P. Henrici (1974) Applied and computational complex analysis, J. Wiley.

    Google Scholar 

  9. W. Seewald (1982) Quotienten-Differenzen-Algorithms: Beweis der Regeln von Rutishauser. Numer. Math. 40, 93–98.

    Article  MathSciNet  MATH  Google Scholar 

  10. W.B. Gragg (1977) Laurent, Fourier and Chebyshev-Padé tables. in Padé and rational approximation ed. by E.B. Saff and R.S. Varga. Ac. Press, New York, 61–72.

    Chapter  Google Scholar 

  11. W.B. Jones, A. Magnus (1980) Computation of poles of two-point Padé approximants and their limits. Journ. Comput. Appl. Math. 6 (2), 105–119.

    Article  MathSciNet  MATH  Google Scholar 

  12. K.M. Day (1975) Toeplitz matrices generated by an arbitrary rational function. Trans. Amer. Math. Soc. 206, 224–245.

    Article  MathSciNet  MATH  Google Scholar 

  13. I.Z. Gochberg, I.A. Feldmand (1974) Faltungsgleichungen und Projektionsverfahren zu ihrer Lösung. Birkhauser Verlag, Basel.

    Book  Google Scholar 

  14. A. Draux (1983) Polynomes orthogonaux formels-applications. Lect. Notes Math. 974, Springer-Verlag, Berlin.

    Book  MATH  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Dept. Computer Sciences, K.U. Leuven, Celestijnenlaan 200A, 3030, Heverlee, Belgium

    Adhemar Bultheel

Authors
  1. Adhemar Bultheel
    View author publications

    You can also search for this author in PubMed Google Scholar

Editor information

Helmut Werner Hans Josef Bünger

Rights and permissions

Reprints and permissions

Copyright information

© 1984 Springer-Verlag

About this paper

Cite this paper

Bultheel, A. (1984). Zeros of a rational function defined by its Laurent expansion. In: Werner, H., Bünger, H.J. (eds) Padé Approximation and its Applications Bad Honnef 1983. Lecture Notes in Mathematics, vol 1071. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0099608

Download citation

  • DOI: https://doi.org/10.1007/BFb0099608

  • Published:

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-13364-3

  • Online ISBN: 978-3-540-38914-9

  • eBook Packages: Springer Book Archive

Publish with us

Policies and ethics

Search

Navigation