A fast algorithm for solving banded Toeplitz systems

A fast algorithm for solving systems of linear equations with banded Toeplitz matrices is presented. This new approach is based on extending the given matrix with several rows on the top and several columns on the right and to assign zeros and some nonzero constants in each of these rows and columns in such a way that the augmented matrix has a lower triangular Toeplitz structure. Stability of the algorithm is discussed and its performance is showed by numerical experiments.