Skip to main content
Log in

Fast inversion algorithms of Toeplitz-plus-Hankel matrices

  • Published:
Numerische Mathematik Aims and scope Submit manuscript

Summary

The paper deals with the problems of fast inversion of matricesA=T+H, whereT is Toeplitz andH is Hankel. Several algorithms are presented and compared, among them algorithms working for arbitrary strongly nonsingular matricesA=T+H.

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

Access this article

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

  1. Bultheel, A.: Laurent series and their Padé approximation. Basel, Boston, Stuttgart: Birkhäuser 1987

    Google Scholar 

  2. Gohberg, I., Kailath, T., Koltracht, I.: Efficient solution of linear systems of equations with recursive structure. Linear Algebra Appl.80, 81–113 (1986)

    Google Scholar 

  3. Heinig, G., Rost, K.: Algebraic methods for Toeplitz-like matrices and operators. Berlin: Akademie-Verlag; Basel, Boston, Stuttgart: Birkhäuser 1984

    Google Scholar 

  4. Heinig, G., Rost, K.: Fast inversion of Toeplitz-plus-Hankel matrices. Wiss. Zeitschrift der TH Karl-Marx-Stadt27, 1 66–71 (1985)

    Google Scholar 

  5. Heinig, G., Rost, K.: On the inverse of Toeplitz-plus-Hankel matrices. Linear Algebra and Its Appl. (to appear 1988)

  6. Iohvidov, I.S.: Hankel and Toeplitz matrices and forms. (Russian) Moscow: Nauka 1974; Basel, Boston, Stuttgart: Birkhäuser 1982

    Google Scholar 

  7. Ljung, S.: Fast algorithms for integral equations and least square identification problem. Linköp. Stud. Sc. Tech., Diss. 93, 1983

  8. Merchant, G.A., Parks, T.W.: Efficient solution of a Toeplitz-plus-Hankel coefficient matrix system of equation. IEEE Transact. on Acoust. Speech Sign. Process.30, 1 40–44 (1982)

    Google Scholar 

  9. Nersesjan, A.B., Papoyan, A.A.: Construction of the matrix inverse to the sum of Toeplitz and Hankel matrices. (Russian) Izv. AN Arm. SSR 18,2: 150–160 (1983)

    Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Rights and permissions

Reprints and permissions

About this article

Cite this article

Heinig, G., Jankowski, P. & Rost, K. Fast inversion algorithms of Toeplitz-plus-Hankel matrices. Numer. Math. 52, 665–682 (1988). https://doi.org/10.1007/BF01395817

Download citation

  • Received:

  • Issue Date:

  • DOI: https://doi.org/10.1007/BF01395817

Subject Classifications

Navigation