An extended Berlekamp-Massey algorithm for the inversion of Toeplitz matrices

The Berlekamp-Massey algorithm (BMA) which solves special Toeplitz systems of linear equations is extended to an algorithm for inverting Toeplitz matrices. The original BMA itself leads to one row of the inverse of the corresponding Toeplitz matrix. The other rows are derived using the same operations that are central to the original BMA. Two alternatives for the extended BMA are presented: the first includes the usual BMA without any changes, and the second simplifies the structure by some modifications also in the original BMA part. Both versions follow a tree-like structure. If the branches of the tree are implemented in parallel, the time demand would be nearly the same as for the usual BMA. In contrast to other Toeplitz algorithms, only slight modifications must be incorporated to handle singular submatrices