Minimum w-entropy interpolants for matricial Carathéodory functions and maximum determinant completions of associated block Pick matrix

The so-called modified block Toeplitz vector approach is used to connect a class of particular solutions Gw for w∈D of a nondegenerate interpolation problem of the Nevanlinna–Pick type with a class of particular solutions Fw of a certain matricial Carathéodory coefficient problem in a transparent way. This will suggest a simple approach to the minimum w-entropy interpolants and the maximum determinant completions of the associated block Pick matrix within the framework of that Nevanlinna–Pick type interpolation problem by using the known assertions corresponding to Fw. It turns out that Gw(w∈D) is exactly or provides us with the unique solution to these two extremal problems in a manner.