Exponential Inequalities in Stochastic Inverse Problems Using an Iterative Method

Abstract

We consider an iterative method in order to solve linear inverse problems. We establish exponential inequalities for the probability of the distance between the approximated solution and the exact one for a calibration problem. The approximate is given by an iterative method with Gaussian errors. We treat an operator equation of the form Ax = u, where A is a compact operator.

Keywords:

• Cramer condition
• Gaussian measure
• Iterative method
• Linear operator
• Tikhonov regularization

Mathematics Subject Classification:

• 65N21
• 53C38Q