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 G_w for w∈D of a nondegenerate interpolation problem of the Nevanlinna-Pick type with a class of particular solutions F_w 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 F_w. It turns out that G_w(w∈D) is exactly or provides us with the unique solution to these two extremal problems in a manner.