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