Thread Rating:
  • 0 Vote(s) - 0 Average
  • 1
  • 2
  • 3
  • 4
  • 5
matrix function like iteration without power series expansion
#3
Gottfried Wrote:Using a matrix-expression this would be

t°h(x) = W^-1 sum k=0..inf sum j=0..k (-1)^j * binomial(k,j) *diag(1,u^j,u^2j,...) * W

sum j=0..k (-1)^j * binomial(k,j) *dV(u^j) = diag(u^j-1) *PPow(
sum k=0..inf
what?

Quote:"not regularly" Euler-summable

Yes, I see. Its somehow similar to your tetra series its only summable via the matrix method for not having an attracting (finite) fixed point, i.e. in our case .

However the aim was to not use the matrix method for computation.
This is faster and does not require the function to be developable into a powerseries. For regular iteration we have both: limit formulas and powerseries coefficient formulas. And now we have also both for the matrix function method (if it can still be called that way for the limit formula).

The limit formula yields exactly the same iterates as the matrix function method if it converges. With this formula its perhaps easier to verify that the matrix function method just gives the regular iteration at the attracting fixed point, though I didnt try to prove this yet.
Reply


Messages In This Thread
RE: matrix function like iteration without power series expansion - by bo198214 - 07/01/2008, 06:48 AM

Possibly Related Threads...
Thread Author Replies Views Last Post
  New mathematical object - hyperanalytic function arybnikov 4 211 01/02/2020, 01:38 AM
Last Post: arybnikov
  Perhaps a new series for log^0.5(x) Gottfried 0 172 12/05/2019, 04:35 PM
Last Post: Gottfried
  Is there a function space for tetration? Chenjesu 0 444 06/23/2019, 08:24 PM
Last Post: Chenjesu
  A Notation Question (raising the highest value in pow-tower to a different power) Micah 8 2,687 02/18/2019, 10:34 PM
Last Post: Micah
  Degamma function Xorter 0 892 10/22/2018, 11:29 AM
Last Post: Xorter
Question Taylor series of i[x] Xorter 12 11,776 02/20/2018, 09:55 PM
Last Post: Xorter
  Functional power Xorter 0 1,333 03/11/2017, 10:22 AM
Last Post: Xorter
  Complaining about MSE ; attitude against tetration and iteration series ! tommy1729 0 1,624 12/26/2016, 03:01 AM
Last Post: tommy1729
  2 fixpoints , 1 period --> method of iteration series tommy1729 0 1,489 12/21/2016, 01:27 PM
Last Post: tommy1729
  2 fixpoints related by power ? tommy1729 0 1,469 12/07/2016, 01:29 PM
Last Post: tommy1729



Users browsing this thread: 1 Guest(s)