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.
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.
[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.
[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.
[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.
[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.
[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.
[T] Trench,W.F., An algorithm for the inversion of finite Toeplitz matrices. SIAM J. Appl. Math. 12, 3 (1964), 515–522.
Author information
Authors and Affiliations
Rights 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
Received:
Issue Date:
DOI: https://doi.org/10.1007/BF01196879