"Roger Stafford" wrote in message <email@example.com>... > "David Epstein" <David.Epstein.firstname.lastname@example.org> wrote in message <email@example.com>... > > @Roger: what were your reasons for rejecting this approach in your randfixedsum package on FEX? > - - - - - - - - - - > I think you will find that as n increases the acceptance rate in such a procedure shrinks toward zero altogether too rapidly, thereby restricting one in practice to a rather small range for n. > > To get a feeling for this, consider an n-dimensional hypersphere of radius 1/2 enclosed in an n-dimensional cube with unit-length sides. The n-dimensional volume of the cube is 1 whereas that of the hypersphere for even n is (pi/4)^(n/2)/(n/2)! (See http://en.wikipedia.org/wiki/N-sphere.) For n = 50 this would be 1.53E-28, a small acceptance rate indeed.
IMHO, the difficulty is in the same order than solving linear programing with the constraints A*y <= b, which have to find accurately the vertices without ambiguity. At least for the convex part.
I have little experience in Delaunay in high dimensional space. But I could imagine it 's challenging too.