Split algorithms for hermitian Toeplitz matrices with arbitrary rank profile

AbstractSplit algorithms for Toeplitz matrices exploit besides the Toeplitz structure additional symmetry properties to reduce the number of operations. In this paper split Levinson and Schur algorithms for hermitian Toeplitz matrices are presented that work, in contrast to previous algorithms, without additional conditions like strong nonsingularity. The main contribution is the generalization of the split Levinson-type algorithms of B. Krishna/H. Krishna and H. Krishna/S. Morgera to general nonsingular hermitian Toeplitz matrices. Furthermore, a Schur-type counterpart of this algorithm is presented that is also new in the strongly nonsingular case. Some auxiliary considerations concerning the kernel structure of hermitian Toeplitz matrices might be of independent interest