%0 Journal Article
%T Numerical Differentiation of 2D Functions by a Mollification Method Based on Legendre Expansion
%A Ou Xie
%A Zhenyu Zhao
%J International Journal of Computer Science Issues
%D 2013
%I IJCSI Press
%X In this paper, we consider numerical differentiation of bivariate functions when a set of noisy data is given. A mollification method based on spanned by Legendre polynomials is proposed and the mollification parameter is chosen by a discrepancy principle. The theoretical analyses show that the smoother the genuine solution, the higher the convergence rates of the numerical solution. To get a practical approach, we also derive corresponding results for Legendre-Gauss-Lobatto interpolation. Numerical examples are also given to show the efficiency of the method.
%K Ill-posed problem
%K Numerical differentiation
%K Legendre spectral method
%K Discrepancy principle.
%K IJCSI
%U http://www.ijcsi.org/papers/IJCSI-10-1-2-729-734.pdf