@techreport{sou-sto-15-msbas-gendisc-tr,
   number = {IC-15-08},
   author = {Gilc{\'e}lia Regi{\^a}ne de Souza and Jorge Stolfi},
   title = {Adaptive  Multiscale  Function  Approximation - {I}: {General} Discrete Bases},
   month = dec,
   year = 2015,
   institution = {Institute of Computing, University of Campinas},
   note = {In English, 22 pages.},
   abstract = {We describe efficient algorithms for adaptive multiscale approximation of functions that are sampled with uneven density and/or have important small-scale detail limited to small portions of their domain. Our algorithms are very general, independent of domain shape, mesh, and approximation basis. A full multiscale basis is defined generically as a hierarchy of single-scale bases, whose elements have progressively smaller supports and are arranged more densely over the domain. An adaptive multiscale basis is a subset of a full one, that excludes elements that contribute very little to the approximation. We tested our algorithms with a hierarchical basis of finite Bézier elements on regular triangular meshes. The tests show that the size of the adaptive basis can be about 1/100 of the size of a full single-scale basis of the same spatial resolution, leading to enormos savings in computation time. (Earlier versions of these algorithms were described in the Ph.~D.~Thesis of the first author.)},
  altkey = {TR-IC-15-08}
}