Filter Transfer Functions for the Method of Successive Corrections

Abstract

The frequency-domain characteristics of the successive corrections method in one dimension are investigated through the calculation of smoother weights and filter transfer functions. The successive corrections algorithm acts as a low-pass filter that behaves similarly to noniterative smoothers. The spectral content of fixed-span successive corrections estimates depends upon the number of iterations, the selected weighting function and the grid to which the dataset is interpolated. For a given weighting function and grid, increasing the number of iterations for the fixed-span case results in filter transfer functions with increased cutoff frequency and rolloff. Within data gaps, the use of more than one iteration leads to estimates that are more likely to be contaminated by high-frequency variability in the data. It is shown that variable-span successive corrections estimates are nearly independent of the choice of weights for the initial iterations and are almost equivalent to estimates obtained using a single iteration. The greater computational requirements of multiple-iteration successive corrections is a disadvantage for general applications.