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# Méthodes inverses

Content of the EU:

1. Introduction.
2. The Lanczös decomposition and inverse of any linear operator. Resolution and Information Matrices. Synthetic tests.
3. Classical least squares method.
4. Conditioning of a linear operator.
5. Probabilistic approach of inverse methods.
6. The inverse stochastic: generalization of the least square inverse. Quality of the inverted model.
7. Generalized least squares for a nonlinear problem.
8. Bayesian approach of the inverse problem.
9. Methods for model space exploration.

Expected: Students must be able to write and program the solution of an inverse problem. They should master the inversion techniques discussed in the course as well as the methods for estimating the quality of the inverse model (Resolution, Information, posterior covariance and synthetic tests). A part of the practicals will be devoted to the numerical processing of examples in Matlab language.

Prerequisites:

• Elementary knowledge in linear algebra:
• Addition, multiplication of matrices, inversion of simple matrices (2x2 or 3x3), knowledge of what is a transposed matrix, the trace of a matrix and how to calculate eigenvectors and eigenvalues.
• Elementary knowledge of probabilities:
• Density of probabilities, marginal probability, conditional probabilities, Gaussian distribution.

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Département ENS
• Directrice :
Guillemette Ménot
• Secrétaire :
Emmanuelle Lousson
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