A fast block Hankel solver based on an inversion formula for block Loewner matrices

We propose a newO(p ³ n ²) algorithm for solving complexnp×np linear systems that have block Hankel structure, where the blocks are square matrices of sizep×p. Via FFTs the block Hankel system is transformed into a block Loewner system. An inversion formula enables us to calculate the inverse of the block Loewner matrix explicitely. The parameters that occur in this inversion formula are calculated by solving two rational interpolation problems on the unit circle. We have implemented our algorithm in Fortran 90. Numerical examples are included.