An augmented iterative method for large linear Toeplitz systems

Efficiently solving a large linear system of equations, Ax = b, is still a challenging problem. Such a system appears in many applications in signal processing, especially in some problems in acoustics where we deal with very long impulse responses, i.e. x is long. In this paper, we show how to efficiently use the so-called basic iterative algorithms when the matrix A is Toeplitz, symmetric, and positive definite. We also propose an improved version that converges much faster than some other iterative methods. We present some simulations and compare the new method to the conjugate gradient algorithm.