To add onto the question, how are elliptical differential equations applicable in this context?

I was listening to a talk about Bayesian networks and someone asked if they were using differential elliptical equations in the context of linear relaxation.

  • 1
    $\begingroup$ What are the results of your results? Can you specify "in the context of" more closely? (I'm sure there more than one application.) $\endgroup$ – Raphael Apr 23 '14 at 6:01
  • $\begingroup$ I don't know about linear relaxation in Bayesian networks, but in inverse problems differential operator regularization (eg, the (graph-) Laplacian) is commonly used to penalize highly oscillatory solutions. That is, you try to make the solution at a point similar to the solution at nearby points. This works because differential operators usually amplify higher frequencies more than lower frequencies. $\endgroup$ – Nick Alger Apr 23 '14 at 16:13
  • $\begingroup$ Thanks for the responses guys, unfortunately this question is actually meaningless–I managed to track down the person and elliptical differentials actually have nothing to do with linear relaxation (he was asking about an old technique to solve diffeqs called relaxation). $\endgroup$ – Jonathan Howard Apr 24 '14 at 21:10