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An Introduction to the Mathematical Theory of Inverse Problems
| Speaker: |
I.A. Lioulina, M.Sc. |
| Date: |
Wednesday March 12, 2003 |
| Title: |
An Introduction to the Mathematical Theory of Inverse Problems |
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Abstract
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| In the first lecture we begin with a list of pairs of direct
and inverse
problems. Many of them are quite elementary and well-known. An
appropriate
mathematical framework for the analysis of inverse problems will be
given.
We introduce the notions of ill-posedness and the worst-case error.
While
ill-posedness of a problem implies that the solution cannot be computed
numerically – which is a very pessimistic point of view – the notation
of the worst-case error leads to the possibility that stability can be
recovered if additional information is available. |
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