Efficient inversion of doubly block Toeplitz matrix

An iterative algorithm for the inversion of a doubly block Toeplitz matrix consisting of m × m blocks of size p × p is described. The algorithm presented exploits the structure of the doubly block Toeplitz matrix and outperforms Akaike's algorithm by a factor of
\max {2 \frac{p}{m},2}
. The use of this algorithm for an iterative solution of a doubly block Toeplitz set of linear equations is also presented.