Inversion of mosaic Hankel matrices via matrix polynomial systems (Q1893120)

A mosaic Hankel matrix is a square matrix which can be partitioned into rectangular blocks, each of which is a Hankel matrix. \textit{G. Heinig} and \textit{A. Tewodros} [Semin. Anal. 88, 53-65 (1988; Zbl 0674.15016)] have given a set of linear equations which determine whether a mosaic Hankel matrix has an inverse together with a tool to compute the inverse when it exists. In the present paper these linear equations are converted to an equivalent matrix polynomial form which corresponds to matrix-type Padé approximants of a related matrix power series. These matrix polynomials are directly related to work of \textit{A. C. Antoulas} [IEEE Trans. Autom. Control AC-31, 1121-1135 (1986; Zbl 0666.93049)]. The final section shows that the inversion problem for a mosaic Hankel matrix can be reduced to inversion of two smaller mosaic Hankel matrices; this leads to an efficient algorithm for computing inverses of such matrices. Details of these results are too complicated to include here.