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 Matrix-method: compare use of different fixpoints Gottfried Ultimate Fellow Posts: 776 Threads: 121 Joined: Aug 2007 11/13/2007, 05:48 PM (This post was last modified: 11/13/2007, 05:54 PM by Gottfried.) bo198214 Wrote:You probably mean B * W(B)[col] = W(B)[col] * d[col] but thats just the matrix version of the Schroeder equation $\sigma(\exp_b(x))=c\sigma(x)$. If you find a solution $\sigma$ to the Schroeder equation you make the Carleman/column matrix $W(B)$ out of it and you have a solution of this infinite matrix equation and vice versa if you have a solution W(B) to the above matrix equation that is the Carleman/column matrix of a powerseries $\sigma$ then this power series is a solution to the Schroeder equation. Nothing new is gained by this consideration. I'm trying to understand the problem of uniqueness now. Since by the eigensystem I do not only have one equation (imaging the meaning of fixpoints) for the first row by W^-1 [,0] * Bs = d[0,0] * W^-1[,0] = 1*W^-1[,0] whose series-expression may not be a non-uniquely determination for f(x) = s^x (or another way round?) (Henryk suggested some examples, for instance a mixture using coefficients of an overlaid sine-function, if I understood this correctly). I have infinitely many equations according to each row of W^-1. Say u = log(t) wheren t^(1/t) = b = base I have also W^-1 [,1] * Bs = u^1*W^-1[,1] W^-1 [,2] * Bs = u^2*W^-1[,2] ... (where the second row happens to express the series for the first derivative w.r. to the topexponent x if I see it right) and so on. The same sine-overlay should not be sufficient to satisfy all these further equations. But this is merely speculation here, since I did not yet understand, in what the uniqueness-problem comes into play. Gottfried Gottfried Helms, Kassel « Next Oldest | Next Newest »

 Messages In This Thread Matrix-method: compare use of different fixpoints - by Gottfried - 11/04/2007, 12:38 PM RE: Matrix-method: compare use of different fixpoints - by bo198214 - 11/04/2007, 12:59 PM RE: Matrix-method: compare use of different fixpoints - by Gottfried - 11/04/2007, 01:28 PM RE: Matrix-method: compare use of different fixpoints - by bo198214 - 11/04/2007, 01:31 PM RE: Matrix-method: compare use of different fixpoints - by Gottfried - 11/04/2007, 01:40 PM RE: Matrix-method: compare use of different fixpoints - by bo198214 - 11/07/2007, 10:52 AM RE: Matrix-method: compare use of different fixpoints - by Gottfried - 11/07/2007, 01:33 PM RE: Matrix-method: compare use of different fixpoints - by bo198214 - 11/07/2007, 01:57 PM RE: Matrix-method: compare use of different fixpoints - by Gottfried - 11/07/2007, 02:10 PM RE: Matrix-method: compare use of different fixpoints - by bo198214 - 11/07/2007, 02:21 PM RE: Matrix-method: compare use of different fixpoints - by Gottfried - 11/07/2007, 02:59 PM RE: Matrix-method: compare use of different fixpoints - by bo198214 - 11/07/2007, 03:35 PM RE: Matrix-method: compare use of different fixpoints - by Gottfried - 11/07/2007, 04:31 PM RE: Matrix-method: compare use of different fixpoints - by bo198214 - 11/07/2007, 07:44 PM RE: Matrix-method: compare use of different fixpoints - by Gottfried - 11/07/2007, 08:41 PM RE: Matrix-method: compare use of different fixpoints - by bo198214 - 11/07/2007, 09:32 PM RE: Matrix-method: compare use of different fixpoints - by Gottfried - 11/11/2007, 06:05 PM RE: Matrix-method: compare use of different fixpoints - by bo198214 - 11/11/2007, 10:05 PM RE: Matrix-method: compare use of different fixpoints - by Gottfried - 11/12/2007, 01:53 AM RE: Matrix-method: compare use of different fixpoints - by Gottfried - 11/13/2007, 05:48 PM RE: Matrix-method: compare use of different fixpoints - by Gottfried - 11/12/2007, 07:48 AM RE: Matrix-method: compare use of different fixpoints - by bo198214 - 11/12/2007, 11:52 AM RE: Matrix-method: compare use of different fixpoints - by Gottfried - 11/12/2007, 03:13 PM RE: Matrix-method: compare use of different fixpoints - by andydude - 11/30/2007, 05:24 PM

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