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 (M − 1)th 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 (M − 1)th order parameters.

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