Superfast Approximative Implementation of the IAA Spectral Estimate

In this correspondence, we develop superfast approximative one-dimensional algorithms for the computationally efficient implementation of the recent iterative adaptive approach (IAA) spectral estimate. The proposed methods are based on rewriting the IAA algorithm with suitable Gohberg-Semencul representations, solving the resulting linear systems of equations using the preconditioned conjugate gradient method, where a novel preconditioning is applied using an incomplete factorization of the Toeplitz matrix. Numerical simulations illustrate the efficiency of both the proposed preconditioning as well as the overall algorithm, offering a computational reduction of up to two orders of magnitude as compared to our recently proposed efficient and exact IAA implementation.