New choices for Tikhonov regularization matrix using fractional
derivative approach
Abstract
A linear discrete ill-posed problem has a perturbed right-hand side
vector and an ill-conditioned coefficient matrix. The solution to
such a problem is very sensitive to perturbation. Replacement of the
coefficient matrix by a nearby one that has less condition number is
one of the well-known approaches for decreasing the sensitivity of the
problem to perturbation. In this paper, we suggest some new
regularization matrix to the Tikhonov regularization. These new ones
are based on fractional derivatives such as Grunwald-Letnikov and Caputo
and can cause to have more exact solutions.