Polopoly will be shut down December 15, 2023. Existing pages will have to be moved before or will be removed at that date. Empolyees may read more at FAQ Polopoly Avveckling
MAI0099
Regularization Theory/
Regulariseringteori
Number of credits: 8 hp
Examiner: Natan Kruglyak
Lecturer: Natan Kruglyak and Fredrik Berntsson
Course literature: Compendium based on the lectures and book: A. Kirsch, An Introduction to the Mathematical Theory of Inverse Problems.
Aim: After the course the student will be able to use concepts and methods of regularisation theory to concrete inverse problems in science and tecnology. This mean that a student which has taken the course is expected to be able:
- understand definitions and properties of Hilbert spaces and operators;
- investigate properties of simple concrete operators;
- find the singular value for concrete operators;
- understand the notion of well-posed and ill-posed problem;
- understand the algorithms of considered regularization methods and apply them to concrete problems using MATLAB;
- describe definitions and derive relations between the central concepts of the course and apply these relations to solve concrete problems;
- interpret, communicate and argue using mathematical notions.
Course contents: Euclidian and Hilbert spaces. Orthonormal systems. Linear, bouded and compact operators. Adjoint operators. Singular value decomposition for compact operators in Hilbert spaces, Ill-posed problems. Linear regression. Least square method. Cutoff and Tikhonov regularization. The discrepancy principle of Morozov. Landweber iteration method. Galerkin and Collocation methods.
Organisation: Lectures and seminars. Compulsory assignments may be given during the course.
Examination: Oral presentation of the MATLAB project and written exam on the theory of inverse problems.
Prerequisites: Basic Linear Algebra and Basic Fourier analysis.
Page manager:
karin.johansson@liu.se
Last updated: 2022-11-14