Inversion of a block Löwner matrix (Q1919482)

Given a block Löwner matrix \[ L= \bigl((y_i-z_j)^{-1} (C_i-D_j) \bigr)_{{i= 0, \dots, m-1 \atop j = 0, \dots, n-1}}, \] where \(C_i\) and \(D_j\) are \(p \times q\) blocks with \(mp = nq\), and \(y_i,z_j \in F\) and \(\{y_0, \dots, y_{m-1}\} \cap \{z_0, \dots, z_{n-1}\}= \emptyset\), one uses the method of UV-reduction for Toeplitz-like operators and derives a simple inversion formula for \(L\). Connections with matrix rational and tangential interpolations are given and the properties of the parameters of inversion formula are examined. Finally some hints about efficient computation are given, matrix continued fraction representations are considered and the (un)attainability or (in)accessibility of interpolation points are examined.