Abstract
The Gohberg-Semencul formula allows one to express the entries of the inverse of a Toeplitz matrix using only a few entries (the first row and the first column) of the matrix, under some nonsingularity condition. In this paper we will provide a two variable generalization of the Gohberg- Semencul formula in the case of a positive definite two-level Toeplitz matrix with a symbol of the form 1 |p|2 where p is a stable polynomial of two variables. We also consider the case of operator-valued two-level Toeplitz matrices. In addition, we propose an approximation of the inverse of a multilevel Toeplitz matrix with a positive symbol, and use it as the initial value for a Hotelling iteration to compute the inverse. Numerical results are included.
Mathematics Subject Classification (2000). 15A09( 47B35, 65F30)
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Koyuncu, S., Woerdeman, H.J. (2012). The Inverse of a Two-level Positive Definite Toeplitz Operator Matrix. In: Dym, H., Kaashoek, M., Lancaster, P., Langer, H., Lerer, L. (eds) A Panorama of Modern Operator Theory and Related Topics. Operator Theory: Advances and Applications(), vol 218. Springer, Basel. https://doi.org/10.1007/978-3-0348-0221-5_17
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DOI: https://doi.org/10.1007/978-3-0348-0221-5_17
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