(11/10/2013, 07:38 PM)Gottfried Wrote:(11/10/2013, 02:45 AM)mike3 Wrote: So do you want me to post the description? I'm also curious: where do you have trouble with regards to Kouznetsov's method?Well, surely to see the description were really nice (understanding & being-able-to-applicate-it even nicer :-) ) but if there is in fact something in it I'd propose to think about making a toolbox of the procedures and make a contract with Wolfram(mathematica) matlab and so on... - and only after this to publish the details.
The other aspect, what trouble I have with understanding the method: it was about 35 years ago that in some boring days of holiday I went to a library and found books about calculus/integration - written much better than those in my calculus-courses in german in my then college-times, such that I nearly became familiar with it. However, after being back home I became weak with this again and up to today I'm nearly illiterate with integration. Then the article even emphazises "Cauchy integration" and "contour integration" - stepping to "Riemann mapping" - and reading that text is then like trying to walk & balance on the pieces of ice in the arctic water... no reliable ground, no redundancy, - so even if I thought I might have got something correct I did not know whether this was true and meaningful to proceed. So I gave up with that text (I tried to step into it again a couple of times but with not much progress so far)...
Often it is only to understand some key-idea of a concept to be able to metabolize it completely, but that didn't happen so far with the above indicated concepts.
Gottfried
You mention about making a "toolbox" for Wolfram Mathematica. Unfortunately, there's a few problems:
1. I'm not sure if the method is efficient enough to make tetration as rapidly computable as would be needed for such a program (right now (without tweaks) it's still not as fast as sheldonison's Kneser method and even that isn't fast enough,
2. I don't have Wolfram Mathematica myself (I can't afford it), so am not familiar with it/could not program anything for it (beyond what you get using Wolfram Alpha, of course). Ditto for Matlab -- can't afford that either and so have never used it. If you sat me down in front of either of these systems, I wouldn't really be able to do much.
3. I'm not sure what practical uses would exist for continuous tetration, which would make this worthwhile for such programs.
4. if you mean make code for the HAM (since it can be used to solve more than just tetration) in general, written in the languages of those programs, that might be interesting, but HAM code might already exist out there and I'm not sure what advantage any I might make would have.
As for the second point, sorry to hear about your situation with regards to knowledge of integration theory. Have you tried to go back and start from the beginning, as opposed to just jumping into the advanced stuff first?