RE: modal interval
Title: Inner and outer enclosures
Dear Friends,
I agree with Alexandre that we seem to be not yet ready to include modal into the proposed standard.
I am personally a big fan of modal techniques, and I have seen excellent and interesting results coming from this approach, but it looks like even most interval folks are not yet well familiar with this methodology, so it is too early to propose this to others.
What we do need is to make sure is that we have modal intervals at the back of our minds so that by selecting a standard, we do not accidentally ruin the potential of using our interval package in modal techniques.
Vladik
P.S. I think that between Arnold and Nate, there is an easily repairable a misunderstanding:
* to Arnold (and to many of us), modal intervals are an idea explored by SIGNA group, Sergey Shary's papers, etc., an idea that by itself does not imply firct checking for monotonicity etc.
* to Nate modal interval techniques mean a very specific (and, as I understand, very efficient) methodology implemented in his software.
I do not think anyone is well familiar with that methdology, and many of us are eager to learn.
So, when Arnold is arguing against specific features of modal intervals, he means modal intervals in the general sense. When Nate argues that Arnold does not know modal intervals, what he means is that Arnold does not know his algorithm well (which of course is true).
Once we realize that these are two different things, I hope most of the misunderstandings will disappear (and the wolf will lie with the lamb as the Good Book predicts :-)