The Levinson principle generally can be used to compute recursively the solution of linear equations. It can also be used to update the error terms directly. This is used to do single-channel deconvolution directly on seismic data without computing or applying a digital filter. Multichannel predictive deconvolution is used for seismic multiple attenuation. In a standard procedure, the prediction-error filter matrices are computed with a Levinson recursive algorithm, using a covariance matrix of the input data. The filtered output is the prediction errors or the nonpredictable part of the data. Starting with the classical Levinson recursion, wehave derived new algorithms for direct recursive calculationof the prediction errors without computing the data covariance-matrix or computing the prediction-error filters. One algorithm generates recursively the one-step forward and backward prediction errors and the L-step forward prediction error, computing only the filter matrices with the highest index. A numerically more stable algorithm uses reduced QR decomposition or singular-value decomposition (SVD) in a direct recursive computation of the prediction errors without computing any filter matrix. The new, stable, predictive algorithms require more arithmetic operations in the computer, but the computer programs and data flow are much simpler than for standard predictive deconvolution.