A general formulation for least-squares problems
Mark F. Flanagan · 2004
We show that many different least-squares problems which have applications in signal processing may be seen as special cases of a more general vector space minimization problem called the minimum norm problem. We show that special cases of the minimum norm problem include: least squares fitting of a finite set of points to a linear equation and to a quadratic equation; the infinite-length MMSE-optimum linear equalizer; the finite-length MMSE-optimum linear equalizer; the steepest descent algorithm and the more practical LMS algorithm for iterative estimation of the finite-length MMSE-optimum linear equalizer for an unknown channel; and the finite-length least-squares-optimum linear equalizer with a forgetting factor. These examples are not exhaustive but are chosen to illustrate the scope of this framework.