03/06/2008, 04:58 PM
Gottfried Wrote:What I've got so far is a good result for the half-iterate, which seems to be exact to more than 20 digits. I've also used a shifting of x->x' to get a triangular matrix with exact terms, where I denote
and with the above then
Wah thats strong tobacco, I just had used a *translation*, for example
this
Computing the half iterate with your triangular matrices corresponds to computing the regular fractional iterate at the corresponding fixed point (to get
And from here you already see variants:
1. You dont need to use a translation. You can use any bijective (analytic) function
2. The matrix operator method is more general. It does not only work at fixed points but also in between where you use the triangulated finite matrices as approximating sequence. So you can use *any* translation and then apply the matrix operator method. And it is quite sure that all those results differ (by a super small amount).
3. And then you can go even a step further and use any (analytic) bijective