School of Science and Technology

Introduction to the theory, numerical methods, and applications of ill-posed problems

Aim of the course

After a successful completion of the course the students will be able to apply mathematical methods for solving inverse and ill-posed problems.

Target group

Graduate students in mathematics and physics.

Entry requirements

Basic undergraduate mathematics courses in linear algebra, calculus, integral equations.


3 triple hours.


Project work with a written report.


Anatoly Yagola (This is an email address )


May 2nd - 4th, 2016


Örebro University, School of Science and Technology, room T219.

Short description

The field of inverse problems has existed in many branches of physics (geophysics), engineering and mathematics (actually the majority of the natural scientific problems) for a long time. Inverse problems theory has been widely developed within the past decades due partly to its importance of applications, the arrival on the scene of large computers and the reliable numerical methods. Examples like deconvolution in seismic exploration, image reconstruction, tomography and parameter identification, all require powerful computers and reliable solution methods to carry out the computation.

Inverse problems consist in using the results of actual observations or indirect measurements to infer the model or the values of the parameters characterizing the system under investigation. A problem is ill-posed according to the French mathematician Hadamard if the solution does not exist, or is not unique, or if it is not a continuous function of the data. Practical inverse problems are typically related with the case that noise in the data may give rise to significant errors in the estimate. Therefore, to suppress the ill-posedness, designing the proper inversion model and developing proper regularization and optimization algorithms play a vital role.

This course gives a basic introduction to the theory and numerical methods for solving ill-posed problems.


1. A.N. Tikhonov, A.V. Goncharsky, V.V. Stepanov, A.G. Yagola. Numerical methods for the solution of ill-posed problems. - Kluwer Academic Publishers, Dordrecht, 1995.

2. A.N. Tikhonov, A.S. Leonov, A.G. Yagola. Nonlinear ill-posed problems. V.1, 2. - Chapman and Hall, London, 1998.

Course organizers

Anatoly Yagola (This is an email address)

Mårten Gulliksson (This is an email address)

Ye Zhang (This is an email address)

See you on Monday (2nd May) in the room T219 at 14.30 for some coffee and sandwiches, lecture starts around 15.