On Fri, May 05, 2023 at 03:22:49PM -0600, Stephen Guerin wrote:
> I think that's the same as when I said "I knew how to solve n-body systems
> with
> particle N^2/2 forces (corrected) with some quadtree or octree optimizations
> to
> get from n^2 to nlog(n)." . Or are you saying something
I think that's the same as when I said "I knew how to solve n-body systems
with particle N^2/2 forces (corrected) with some quadtree or octree
optimizations to get from n^2 to nlog(n)." . Or are you saying something
different?
On Fri, May 5, 2023 at 2:58 PM Angel Edward wrote:
> Here’s another
Here’s another connection I had forgotten. Consider particles on a 2D rectangle
with 1/r^2 repulsion. If you break up the rectangle into smaller rectangles in
which particles can only stay in their own rectangles or move to neighbor
rectangles, the N^2 force calculation comes down to N log N,
Thanks Roger and Ed!
I've spent some time with Ed and Frank discussing this and I've really
filled in some gaps in my knowledge of parallel algorithms. eg, I knew how
to solve n-body system with particle N^2/2 focus with some quadtree or
octree optimizations to get from n^2 to nlog(n). But the
Most of my dissertation (1968) was on numerical solution of potential problems.
One of the parts was a proof that some of the known iterative methods
converged. The argument loosely went something like this. Consider the 2D
Poisson equation on a square. If you use an N x N approximation with
a quaternion version of Euler's formula
https://www.youtube.com/watch?v=dvpAFWBVgy0
A bit late for the discussion, and kind of sketchy when you get into it.
-Roger
> On Apr 28, 2023, at 8:18 AM, Stephen Guerin
> wrote:
>
> Special Unitary Groups and Quaternions
>
> Mostly for Ed from the
Special Unitary Groups and Quaternions
Mostly for Ed from the context of last week's Physical Friam if you're
coming today.
Discussion was around potential ways of visualizing the dynamics of SU(3),
SU(2), (SU1) that highlights Special Unitary Groups. (wiki link from Frank
