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April 30th, 2015, 06:59 PM  #1 
Newbie Joined: Apr 2015 From: japan Posts: 1 Thanks: 0  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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