Skip to main content
Log in

Inversion of matrices with displacement structure

  • Published:
Integral Equations and Operator Theory Aims and scope Submit manuscript

Abstract

Inversion formulas and fast inversion algorithms for matrices the entries of which fulfil a difference equation are established. In that way the Gohberg/Semencul and Gohberg/Krupnik theorems and related results will be generalized.

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.

Similar content being viewed by others

References

  • [A] Abukov, W.M., Kernel structure and the inversion of Toeplitz and Hankel matrices. (in Russian) Izvestija vuzov (Mat.) 7, 290 (1986), 3–8.

    Google Scholar 

  • [DGK] Delsarte,P.; Genin,Y.V. and Kamp,Y.G., A generalization of the Levinson algorithm for Hermitian Toeplitz matrices with any rank profile. IEEE Trans. Acoust., Speech, Sign. Proc. 33, 4 (1985), 964–971.

    Google Scholar 

  • [GK] Gohberg,I. and Krupnik,N.Ja., A formula for the inversion of finite-section Teoplitz matrices. (in Russian) Mat. Issled. 7, 2 (1972), 272–284.

    Google Scholar 

  • [GS] Gohberg,I. and Semencul,A.A., On inversion of finitesection Toeplitz matrices and their continuous analogues. (in Russian) Mat. Issled. 7, 2(1972), 201–224.

    Google Scholar 

  • [HR1] Heinig,G. and Rost,K., Algebraic methods for Toeplitzlike matrices and operators. Akademie-Verlag, Berlin 1984 and Birkhäuser Verlag, Basel (OT,vol.13) 1984.

    Google Scholar 

  • [HR2] Heinig, G. and Rost,K., Matrices with displacement structure, generalized Bezoutians, and Moebius transformations. (to appear in the Gohberg anniversary volume of the OT series)

  • [L] Levinson,N., The Wiener RMS (root mean square) error criterion in filter design and prediction. J. Math. Phys. 25 (1947), 261–278.

    Google Scholar 

  • [T] Trench,W.F., An algorithm for the inversion of finite Toeplitz matrices. SIAM J. Appl. Math. 12, 3 (1964), 515–522.

    Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Rights and permissions

Reprints and permissions

About this article

Cite this article

Heinig, G., Rost, K. Inversion of matrices with displacement structure. Integr equ oper theory 12, 813–834 (1989). https://doi.org/10.1007/BF01196879

Download citation

  • Received:

  • Issue Date:

  • DOI: https://doi.org/10.1007/BF01196879

Keywords

Navigation