Convergence rates for linear and nonlinear inverse problems in Hilbert spaces via Holder stability estimates

Gaurav Mittal, Ankik Kumar Giri

Published 2018-12-29Version 1

In this article, we look for a new kind of smoothness concept, i.e. Holder smoothness condition for finding the convergence rates of linear and nonlinear inverse problems in Hilbert spaces. The dependency of variational inequalities on the non-linearity estimates satisfied by F for obtaining the convergence rates is also shown. For linear problems, the convergence rates are obtained without the use of the spectral theory and results obtained are similar to [3]. The co-action between the variational inequalities and the Holder stability estimates is also discussed for both the linear and non-linear problems.