Tk. Ku et Ccj. Kuo, PRECONDITIONED ITERATIVE METHODS FOR SOLVING TOEPLITZ-PLUS-HANKEL SYSTEMS, SIAM journal on numerical analysis, 30(3), 1993, pp. 824-845
The use of preconditioned iterative methods to solve a system of equat
ions with a Toeplitz-plus-Hankel coefficient matrix is studied. A new
preconditioner suitable for Toeplitz-plus-Hankel matrices is proposed,
and the spectral properties of preconditioned rational Toeplitz-plus-
Hankel matrices are examined. It is shown that the eigenvalues of the
preconditioned matrix are clustered around unity, except for a finite
number of outliers, depending on the orders of the rational generating
functions, and the clustering radius is proportional to the magnitude
of the last elements in Toeplitz and Hankel matrices. With the spectr
al regularities, an N x N rational Toeplitz-plus-Hankel system can be
solved by preconditioned iterative methods with O(N log N) operations.
Numerical experiments are given to demonstrate the efficiency of the
proposed preconditioner.