280390 VO MA PE 01 VO Inverse Problems (NPI) (2019W)

The course deals with the resolution of ill posed problems (inverse problems from physics, but also, depending on the students, simple problems from data science of data fitting type). More precisely, the following aspects will be presented:
-- Linear regression (and statistical aspects of least squares)
-- Discretization of inverse problems (mainly integrals)
-- Ill posed problems and rank deficiency
-- Tikhonov regularization
-- Nonlinear regression (Newton method,...).
-- Bayesian approach

All these chapter will be complemented with exercises (Matlab or Python).