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 matrix function like iteration without power series expansion Gottfried Ultimate Fellow Posts: 764 Threads: 118 Joined: Aug 2007 07/08/2008, 06:23 PM (This post was last modified: 07/08/2008, 06:26 PM by Gottfried.) Henryk - I crosschecked some results of your method against the diagonalization-method. I got some differences, which look somehow suspicious to me. Using, for instance, u = 0.9 (to be near at a critical value) t = exp(u) = 2.45960311116 b = t^(1/t) = 1.44182935647 I got y = b°0.5(1) = 1.25590667... where in these digits no difference appear. But I got differences in less significant digits, which -as I said- look suspicious: either my summation-methods are not perfect (in fact they give different approximations - I'm still searching for better ones), or I need simply more terms (opposite to the impression). They stabilize (using 96 terms) with differences in the last partial sums of order 1e-18 to 1e-22. So they seem to give usable results. However, the difference to your binomial-method y - y ~ 0.00000000259698761292 is so large compared to the summation-internal inaccurcy, that this seems to be systematic. Different summation-methods gave different result even worse - so in any case I've to improve my summation for these type of divergent series. For t=2, b=sqrt(2) it was much better, but possibly things were simply not visible... I hope I can locate (and possibly remove) the source of the difference... Gottfried Gottfried Helms, Kassel « Next Oldest | Next Newest »

 Messages In This Thread matrix function like iteration without power series expansion - by bo198214 - 06/30/2008, 03:01 PM RE: matrix function like iteration without power series expansion - by Gottfried - 06/30/2008, 09:23 PM RE: matrix function like iteration without power series expansion - by bo198214 - 07/01/2008, 06:48 AM RE: matrix function like iteration without power series expansion - by Gottfried - 07/01/2008, 02:18 PM RE: matrix function like iteration without power series expansion - by Gottfried - 07/02/2008, 11:23 AM RE: matrix function like iteration without power series expansion - by Gottfried - 07/08/2008, 06:56 AM RE: matrix function like iteration without power series expansion - by andydude - 07/08/2008, 06:01 PM RE: matrix function like iteration without power series expansion - by andydude - 07/08/2008, 09:35 PM RE: matrix function like iteration without power series expansion - by Gottfried - 07/08/2008, 06:23 PM RE: matrix function like iteration without power series expansion - by Gottfried - 07/09/2008, 08:58 AM RE: matrix function like iteration without power series expansion - by andydude - 07/09/2008, 02:38 PM RE: matrix function like iteration without power series expansion - by andydude - 07/09/2008, 02:57 PM RE: matrix function like iteration without power series expansion - by bo198214 - 07/09/2008, 06:18 PM RE: matrix function like iteration without power series expansion - by andydude - 07/14/2008, 06:21 PM RE: matrix function like iteration without power series expansion - by bo198214 - 07/14/2008, 09:55 PM RE: matrix function like iteration without power series expansion - by Gottfried - 07/10/2008, 07:01 AM

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