Multilevel least squares approximation of scattered data over binary triangulations

An adaptive method for approximating huge scattered data sets is presented. The approximation scheme generates multilevel triangulations obtained using a subdivision scheme known as longest edge bisection. Nested function spaces are defined over the multilevel triangulations. The approximation problem is solved by successive refinement of the triangulation while iterative methods are used for solving a system of linear equations at intermediate levels of the multi-level scheme. Regularization terms are coupled with a standard least squares formulation to guarantee uniqueness and control smoothness of the solution.