Computational experience with Marple’s algorithm for autoregressive spectrum analysis

Abstract

In 1980 two different recursive algorithms were published, complete with Fortran programs, for autoregressive (AR) spectral estimation, based on least‐squares solutions for the AR parameters using forward and backward linear prediction. The first of these to appear, by Barrodale and Erickson (1980a, b) forms the normal equations for the Mth order AR parameters from the corresponding normal equations for the [Formula: see text] order parameters. However, for each value of M = 1, 2, …, MMAX, the normal equations are solved by Cholesky’s method ab initio, i.e., without reference to the solution of the previous normal equations of lower order. In contrast, the later algorithm by Marple (1980) calculates the Mth order AR parameters in a recursive manner from the [Formula: see text] order parameters.

A Comprehensive Review of Emerging Computational Methods for Gene Identification

“…The model parameters are found by solving a set of linear equations that are obtained by minimizing the mean squared error term (the white noise power) over the data [26]. In addition, the recursive Marple algorithm [27,28] is often utilized for the order selection in autoregressive spectral analysis and estimating the power spectrum density of the AR model.…”