Function Estimation Using A Data-Adaptive Laplacian Smoother.

Abstract

In several applications of Nash iteration for solving nonlinear PDES, it is
customary to use approximate smoothing, based on the solution of evolution equations
with calibrated time steps. The aim of this work is to present a simple adaptive smoothing
procedure based on the solutions of Dirichlet boundary-value problems. The smoother is
an improvement of procedures used,among other applications, in optimization problems
in image processing. This work presents a description of the method and some numerical
tests. A simple nonlinear one dimensional PDE is solved using a Nash iteration scheme
on order to ilustrate the use of this approximate smoothing.