solving problems without clear polynomials: strange functions with
- To: mathgroup at smc.vnet.net
- Subject: [mg78522] solving problems without clear polynomials: strange functions with
- From: Roger Bagula <rlbagula at sbcglobal.net>
- Date: Tue, 3 Jul 2007 05:40:03 -0400 (EDT)
I have two examples of problems that I find hard using FindRoot
mostly for findind the start point a search range:
1) Using this pre-Solve I get a starting range
Solve[7.624706741199758*10^53 *(2.3586540063095223*10^(-11)* a)^2 -
7.514683570223143*10^10 == 0, a]
For
FindRoot[7.624706741199758*10^53 *Erfi[2.3586540063095223*10^(-11)*
a]^2 - 7.514683570223143*10^10 == 0, {a, 0,
1.3310045443281747*10^(-11)}]
I think the answer may be closer to the rational:
1/(3*c)=1.1118801615561874*10^-11
2) The Gamma or factorial to quadratic solve Snand An type groups to
Cartan A_n groups:
a0 = Table[{x /. FindRoot[(x - 1)^2 - 1 - (x - 1)!/n == 0, {x, 3, 20}],
n}, {n, 2, 20}]
ListPlot[a0, PlotJoined -> True]
b0 = Table[{x /. FindRoot[(x - 1)^2 - 1 - (x - 1)!/n == 0, {x, 3, 20}],
n}, {n, 1, 20}]
ListPlot[b0, PlotJoined -> True]
A much better solution in terms of integers is:
c0 = Table[{x /. FindRoot[(x - 1)^2 - 1 - (x)!/n == 0, {x, 3, 20}], n},
{n, 1, 20}]
ListPlot[c0, PlotJoined -> True]
But the answer I was looking for in terms of symmetric groups Sn and An
and Cartan A_n groups is:
d0 = Table[{x /. FindRoot[(x + 1)^2 - 1 - (x)!/n == 0, {x, 3, 20}], n},
{n, 1, 20}]