Course description

Aim. Study of methods for the investigation and the numerical solution of linear and non-linear ill-posed problems on the example of inverse problems.

Short description. The study makes familiar with various questions of the investigation and the numerical solution of inverse problems. The main attention pays to inverse problems of the boundary value reconstruction (the linear case) and the boundary reconstruction (the non-linear case) in the potential theory. Firstly, we consider some general questions for the numerical solution of ill-posed problems in the operator form. Next, considered numerical methods are using for the solution of various inverse problems of the potential theory.

Objects. To be familiar with linear and non-linear ill-posed problems of mathematical physics, numerical methods for their solution and recommendations of their application.

As result after the study student must

• know: regularization methods for linear and non-linear ill-posed problems;
• be able: to apply regularization methods for the solution of various linear and non-linear problems, to build own program products.