I do not have too much to say about the new programme to use SDP to solve EDP, other than that it is still being actively pursued. One remark I would make is that I have rather forgotten recently about keeping the wiki updated, and SDP is a major omission from it. It would be good to have a theoretical account of the method (which I suppose I could paste quite easily from one of my existing posts), and an experimental page devoted particularly to data connected with this approach, with links to all the matrices, sequences and plots that have been produced.
So far, the data has had some expected features (such as the sequence values tending to be larger when is smooth) and some puzzling ones (such as the fact that is much much larger than ). An initial hope for the method was that the experimental data would give rise to a very precise conjecture, but so far that has not happened. There are, however, various avenues that have not been fully explored, and I still have some hope that we will suddenly stumble on some data that we can fully understand. (more…)