Thread Rating:
  • 0 Vote(s) - 0 Average
  • 1
  • 2
  • 3
  • 4
  • 5
Matrix-method: compare use of different fixpoints
#3
bo198214 Wrote:I dont get it. Isnt the matrix decomposition independent of the fixed point?

It means, we can have different eigenmatrices / sets of eigenvectors resulting in the same composition for the infinite matrix Bs. This agrees with the fact, that we have multiple fixpoints for a base s.
For e^-e < s < e^(1/e) we have even two real fixpoints; for other s the fixpoints are complex.

So we may write ( I assume the continuation to more than two solutions)

Bs = W0 * D0 * W0^-1
= W1 * D1 * W1^-1
= W2 * D2 * W2^-1

where W0 and D0 are different to W1 and D1 (and assumed to W2 and D2,...) according to the different initialization with different fixpoints
Gottfried Helms, Kassel
Reply


Messages In This Thread
RE: Matrix-method: compare use of different fixpoints - by Gottfried - 11/04/2007, 01:28 PM

Possibly Related Threads...
Thread Author Replies Views Last Post
  The Promised Matrix Add On; Abel_M.gp JmsNxn 2 561 08/21/2021, 03:18 AM
Last Post: JmsNxn
  Revisting my accelerated slog solution using Abel matrix inversion jaydfox 22 30,989 05/16/2021, 11:51 AM
Last Post: Gottfried
  Which method is currently "the best"? MorgothV8 2 7,711 11/15/2013, 03:42 PM
Last Post: MorgothV8
  "Kneser"/Riemann mapping method code for *complex* bases mike3 2 10,047 08/15/2011, 03:14 PM
Last Post: Gottfried
  An incremental method to compute (Abel) matrix inverses bo198214 3 13,092 07/20/2010, 12:13 PM
Last Post: Gottfried
  SAGE code for computing flow matrix for exp(z)-1 jaydfox 4 13,323 08/21/2009, 05:32 PM
Last Post: jaydfox
  regular sexp:different fixpoints Gottfried 6 18,323 08/11/2009, 06:47 PM
Last Post: jaydfox
  Convergence of matrix solution for base e jaydfox 6 14,368 12/18/2007, 12:14 AM
Last Post: jaydfox



Users browsing this thread: 1 Guest(s)