1. A method for digital signal processing (wherein ‘digital’ refers to the nature of the computational processing and ‘signal’ refers to analog electromagnetic waveforms) on devices employing at least one adaptive processor that employs large numbers of adaptation weights for any adaptation criterion of the set of signal estimation, parameter estimation, measured quality, and any combination thereof for “adapt-path” operations used to tune the adaptive processor, not “data-path” operations used by the adaptive processor during and after tuning, said method comprising: for each adaptation event having M-dimensions, performing a dimensionality reduction comprising a linear transformation of the processor parameters being adapted from M-dimensions to (M 1 +L)-dimensions in each adaptation event, said linear transformation further comprising: adapting M 1 weights without constraints; and, adapting M 0 =M−M 1 weights subjected to L soft constraints forcing them into an L-dimensional subspace spanned by the those weights; applying the same dimensionality reduction to input data using the same linear transformation; and, adapting the reduced-dimensionality weights using the same optimization strategy employed by the adaptive processor, except with the input data to which the same dimensionality reduction has been applied.