Fast algorithms for close-to-Toeplitz-plus-Hankel systems of equation

The authors extend the low-displacement rank definition of close-to-Toeplitz (CT) matrices to close-to-Toeplitz-plus-Hankel (CTPH) matrices and develop fast algorithms for solving CTPH systems of equations. A matrix is defined as CTPH if it is the sum of a CT matrix and a second CT matrix postmultiplied by an exchange matrix; an equivalent definition in terms of UV rank is also given. This definition is motivated by the application of the algorithms to two-sided prediction in which both past and future time-series values are used to estimate the present value.<>