Numerical Solution of the Cauchy Problem for the Laplace Equation: A Deterministic and Bayesian Approach

== Summary ==

We consider a statistical inversion computational model with Gaussian distributions for the numerical solution of the Cauchy problem for the Laplace equation. The a priori model is built up from Gaussian Markov random fields. Different precision matrices for the Cauchy problem are introduced. We take advantage of the relationship between the a priori distribution and traditional Tikhonov regularization to propose different models where smooth and non-smooth regularization is possible. A low range analysis allow us to estimate the optimal dimension of data and its relation to the the unknown.
                                                                                                
== Video ==
{{#evt:service=cloudfront|id=259149|alignment=center|filename=437.mp4}}
                                                
== Abstract ==
<pdf>Media:Draft_Content_652313104A_IDC6_437.pdf</pdf>

== Document ==
<pdf>Media:Draft_Content_652313104_6637_P_IDC6_437.pdf</pdf>