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In this paper, the authors develop superfast approximate 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 using 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 the proposed algorithm. Computationally efficient high-resolution spectral estimation algorithms are of great importance in numerous applications. Typically, to achieve improved resolution, higher than the periodogram, one has to resort to using parametric or data-adaptive non-parametric estimation techniques.
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