An efficient algorithm for solving general periodic Toeplitz systems

An efficient algorithm is presented for inverting matrices which are periodically Toeplitz, i.e., whose diagonal and subdiagonal entries exhibit periodic repetitions. Such matrices are not per symmetric and thus cannot be inverted by Trench´s (1964) method. An alternative approach based on appropriate matrix factorization and partitioning is suggested. The algorithm provides certain insight on the formation of the inverse matrix, is implementable on a set of circularly pipelined processors and, as a special case, can be used for inverting a set of block Toeplitz matrices without requiring any matrix operation