AN EFFICIENT ALGORITHM FOR SOLVING GENERAL PERIODIC TOEPLITZ-SYSTEMS

An efficient algorithm is presented for inverting matrices which are p eriodically Toeplitz, i.e., whose diagonal and subdiagonal entries exh ibit periodic repetitions. Such matrices are not per symmetric and thu s cannot be inverted by Trench's method. An alternative approach based on appropriate matrix factorization and partitioning is suggested. Th e algorithm provides certain insight on the formation of the inverse m atrix, is implementable on a set of circularly pipelined processors an d, as a special case, can be used for inverting a set of block Toeplit z matrices without requiring any matrix operation.