On Apr 30, 2:17 am, Bill Hart <goodwillh...@googlemail.com> wrote: > Actually, I lie, slightly. I did find one instance of `numerical > stability' used in reference to the FFT, and that is on wikipedia (so > now we all know it must be true).
Again, Accuracy and stability of numerical algorithms By Nicholas J. Higham I think that what you might say more precisely is that some ordering of operations to compute the Fourier transform provide more accurate results than some others. That does not mean that they are unstable. Here is a very stable algorithm to compute pi, to n digits. compute_pi(n):= return(22/7). The result is perfectly stable and perfectly precise. It just happens to be inaccurate. > > What I imagine is the correct way of looking at the problem is via > pontrjagin duality, where the group algebras of Z/nZ and its dual are > isomorphic via the fourier transform. I have almost no idea what this means, but I doubt that it has much bearing on numerical approximation. -- To post to this group, send an email to sage-devel@googlegroups.com To unsubscribe from this group, send an email to sage-devel+unsubscr...@googlegroups.com For more options, visit this group at http://groups.google.com/group/sage-devel URL: http://www.sagemath.org
