Schur-type Algorithms for the Solution of Hermitian Toeplitz Systems via Factorization
Georg Heinig, Karla Rost · Birkhäuser Basel eBooks · 2005
In this paper fast algorithms for the solution of systems T u = b with a strongly nonsingular hermitian Toeplitz coefficient matrix T via different kinds of factorizations of the matrix T are discussed. The first aim is to show that ZW-factorization of T is more efficient than the corresponding LU-factorization. The second aim is to design and compare different Schurtype algorithms for LU- and ZW-factorization of T . This concerns the classical Schur-Bareiss algorithm, 3-term one-step and double-step algorithms, and the Schur-type analogue of a Levinson-type algorithm of B. Krishna and H. Krishna. The latter one reduces the number of the multiplications by almost 50% compared with the classical Schur-Bareiss algorithm.