Applications of the Backus-Gilbert method to linear and some non linear equations
Numerical Analysis
2020-12-01 v1 Numerical Analysis
Abstract
We investigate the use of a functional analytical version of the Backus-Gilbert Method as a reconstruction strategy to get specific information about the solution of linear and slightly non-linear systems with Frech\'et derivable operators. Some a priori error estimates are shown and tested for two classes of problems: a nonlinear moment problem and a linear elliptic Cauchy problem. For this second class of problems a special version of the Green-formula is developed in order to analyze the involved adjoint equations.
Cite
@article{arxiv.2011.14407,
title = {Applications of the Backus-Gilbert method to linear and some non linear equations},
author = {A. Leitao},
journal= {arXiv preprint arXiv:2011.14407},
year = {2020}
}
Comments
15 pages, 6 figures