Book chapter
The Inverse of a Two-level Positive Definite Toeplitz Operator Matrix
A Panorama of Modern Operator Theory and Related Topics, pp 387-401
03 Jan 2012
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.
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Details
- Title
- The Inverse of a Two-level Positive Definite Toeplitz Operator Matrix
- Creators
- Selcuk Koyuncu - Drexel UniversityHugo J. Woerdeman - Drexel University
- Publication Details
- A Panorama of Modern Operator Theory and Related Topics, pp 387-401
- Series
- Operator Theory: Advances and Applications
- Publisher
- Springer Basel; Basel
- Resource Type
- Book chapter
- Language
- English
- Academic Unit
- Mathematics
- Other Identifier
- 991021864941404721