@techreport{sou-sto-17-msbas-tens-tr,
   number = {IC-17-01},
   author = {Gilc{\'e}lia Regi{\^a}ne de Souza and Jorge Stolfi},
   title = {Adaptive  Multiscale  Function  Approximation - {II}: {Regular} Tensorial Bases},
   month = jan,
   year = 2017,
   institution = {Institute of Computing, University of Campinas},
   note = {24 pages.},
   abstract = {We apply the general top-down algorithm for adaptive multiscale approximation HApp, described in the Part I of this article, to a specific type of function approximation bases which we call regular multiscale bases. The algorithm guarantees a specified maximum approximation error at every sampling point. While the resulting adaptive basis is not necessarily minimal, it can be much smaller than the full basis, for target functions with localized detail at various spatial resolution scales. The bases elements are tensorial splines with compact support. These bases are similar to standard wavelet bases, except that they provide explicit analytic formulas for the approximating function; that can be used, for example, for differentiation and interpolation between the sampling points. In this part of the article, we assume a regular grid of sampling points and a box-like domain with toroidal topology. These choices allow considerable savings of computing time. We also use at each level a modified least squares analysis operator with Bayesian outlier rejection.},
  altkey = {IC-17-01}
}