# On 2D Inverse Problems/An infinite example

${\displaystyle \Lambda _{G}={\sqrt {L}}.}$
(Hint:) Use the fact that the operator/matrix is the fixed point of the Schur complement]]: ${\displaystyle \Lambda _{G}={\begin{pmatrix}2I&B\\B^{T}&\Lambda +2I\end{pmatrix}}/(\Lambda +2I),}$ where ${\displaystyle B=-{\begin{pmatrix}1&0&0&\ldots &1\\1&1&0&\ldots &0\\0&\vdots &\ddots &\ddots &\vdots \\\vdots &\vdots &\ddots &1&0\\0&0&\ldots &1&1\\\end{pmatrix}}}$ is the circulant matrix, such that ${\displaystyle L_{G}=4I-BB^{T}.}$