08/28/2007, 08:20 AM
Finally, I'll show some of the things I'm looking at at the moment. For starters, here's a graph of the 300-, 400-, 500-, and 560-term solutions, graphing the even terms of the derivative (i.e., based off the odd terms of the original power series). I've reverse the signs on alternating terms, and I've scaled by the same 1.374 factor as before:
See how the series seem to converge to some cyclic "curve"? I say curve, though it's a discrete set of points that I've artificially connected. Currently, I'm trying to work with the limited data I have to figure out what values each of these peaks approaches. I would like to ask if anyone has a machine/math library capable of solving a 600x600, 640x640, or even 700x700 system, to get more data points to work with. (If anyone has a library capable of solving an 800x800 system in less than a week, I'd very much appreciate seeing the results.) I don't need a lot of precision, though you'd need to solve the system exactly with rational math to ensure quality, then reduce the values to e.g. 100 digits or even just double precision so we could analyze further.
See how the series seem to converge to some cyclic "curve"? I say curve, though it's a discrete set of points that I've artificially connected. Currently, I'm trying to work with the limited data I have to figure out what values each of these peaks approaches. I would like to ask if anyone has a machine/math library capable of solving a 600x600, 640x640, or even 700x700 system, to get more data points to work with. (If anyone has a library capable of solving an 800x800 system in less than a week, I'd very much appreciate seeing the results.) I don't need a lot of precision, though you'd need to solve the system exactly with rational math to ensure quality, then reduce the values to e.g. 100 digits or even just double precision so we could analyze further.
~ Jay Daniel Fox