  We present a generalized formulation for reweighted least squares
approximations. The goal of this article is twofold: firstly, to prove that the
solution of such problem can be expressed as a convex combination of certain
interpolants when the solution is sought in any finite-dimensional vector
space; secondly, to provide a general strategy to iteratively update the
weights according to the approximation error and apply it to the spline fitting
problem. In the experiments, we provide numerical examples for the case of
polynomials and splines spaces. Subsequently, we evaluate the performance of
our fitting scheme for spline curve and surface approximation, including
adaptive spline constructions.
