Local inversion of matrices with sparse inverses (Q1307520)

If \(G\) is a chordal graph and the inverse \(A^{-1}\) of a matrix \(A\) is subordinate to \(G\), then \(A^{-1}\) can be computed from the primary entries of \(A\). Here a matrix \(B=(b_{ij})\) is called subordinate to \(G\) if \(\{i,j\}\) is not an edge in \(G\) implies that \(b_{ij}=0\). The primary entries of \(A\) are the diagonal ones and those \(a_{ij}\) with \((i,j)\) an edge of \(G\).