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April 30th, 2015, 06:59 PM   #1
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inverse of semi infinite toeplitz matrix

Hi all,

I have a semi infintie toeplitz matrix of the form

$\displaystyle A=\left(\begin{array}{ccccc}
A_{0} & A_{1} & 0 & 0 & \cdots\\
A_{-1} & A_{0} & A_{1} & 0 & \cdots\\
0 & A_{-1} & A_{0} & A_{1} & \cdots\\
0 & 0 & A_{-1} & A_{0} & \cdots\\
\vdots & \vdots & \vdots & \vdots & \ddots
\end{array}\right) $,
where $\displaystyle A_{0}$, $\displaystyle A_{1}$ and $\displaystyle A_{-1}$ are finite n by n matrices. First is it possible to calculate the inverse $\displaystyle A^{-1} $ of $\displaystyle A$ ? And second can one obtaine the upper left n by n block of the inverse ?

Best,
Marius
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