Thread Rating:
  • 0 Vote(s) - 0 Average
  • 1
  • 2
  • 3
  • 4
  • 5
An incremental method to compute (Abel) matrix inverses
I fiddled a bit around with Gottfried's suggestion of LU decomposition of the Abel matrix (though in the end the formula is independent of the LU decomposition).

The annoying thing about calculating the intuitive Abel function (by solving the equation Ax=b where A is the Abel matrix, x the powerseries development of the Abel function and b=(1,0,...)) that if you want to increas the matrix size you have to solve the complete equation again without being able to use your previous solution.

Now I found a way how you can compute the inverse of the matrix by using the Abel matrix. I dissect the matrix as follows, for brevity I set :

means column vector and means row vector.

The final incremental formula is then:

Where means adding the entry 1 to the vector and is extended to a nxn matrix by filling with 0's.

The deriviation is perhaps too uninteresting and cumbersome to put, but I can post it if inquired.

Messages In This Thread
An incremental method to compute (Abel) matrix inverses - by bo198214 - 07/09/2010, 06:31 AM

Possibly Related Threads...
Thread Author Replies Views Last Post
  Revisting my accelerated slog solution using Abel matrix inversion jaydfox 21 8,127 02/09/2019, 02:25 PM
Last Post: sheldonison
  Which method is currently "the best"? MorgothV8 2 4,625 11/15/2013, 03:42 PM
Last Post: MorgothV8
  "Kneser"/Riemann mapping method code for *complex* bases mike3 2 6,605 08/15/2011, 03:14 PM
Last Post: Gottfried
  Attempting to compute the kslog numerically (i.e., Kneser's construction) jaydfox 11 18,062 10/26/2009, 05:56 PM
Last Post: bo198214
  SAGE code for computing flow matrix for exp(z)-1 jaydfox 4 8,197 08/21/2009, 05:32 PM
Last Post: jaydfox
  Convergence of matrix solution for base e jaydfox 6 8,752 12/18/2007, 12:14 AM
Last Post: jaydfox
  Computing Abel function at a given center jaydfox 10 12,092 11/30/2007, 06:44 PM
Last Post: andydude
  Matrix-method: compare use of different fixpoints Gottfried 23 23,881 11/30/2007, 05:24 PM
Last Post: andydude

Users browsing this thread: 1 Guest(s)