Ill-posed problems

Entry requirements
Basic undergraduate mathematics courses in linear algebra, calculus, integral equations.
Course organizers
Anatoly Yagola (yagola@physics.msu.ru ) and Larisa Beilina (larisa.beilina@chalmers.se )
Teachers
Anatoly Yagola (yagola@physics.msu.ru )
Course program
1)Elements of the theory of ill-posed problems . Ill-posed problems in physical sciences.
Definitions. Functional spaces and linear operators. Regularizing algorithms. Fundamental
properties of ill-posed problems. Ill-posed problems on compact sets. Sourcewise representation
and a posteriori error estimation. Tikhonov’s variational approach for constructing regularizing
algorithms. Choice of a regularization parameter.
2)Numerical methods for solving ill-posed problems with different constraints. Ill-posed
problems on compact sets of a special structure. Methods for minimization of
Tikhonov’s functional and the discrepancy. Conjugate gradients method and others.
3)Applications to inverse problems of astrophysics, electronic microscopy, acoustics,
astrophysics, geophysics.
Lectures
7 double hours.
Exam
Project work with a written report.