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 the inconsistency depending on fixpoint-selection bo198214 Administrator Posts: 1,389 Threads: 90 Joined: Aug 2007 03/07/2008, 10:56 AM Gottfried Wrote:Code:G0=                                          |G1=                                                   1    .     .      .      .       .         |    1     .     .       .      .       .         0  3/2     .      .      .       .         |    0   3/2     .       .      .       .         0  1/4   9/4      .      .       .         |    0  -1/4   9/4       .      .       .         0    0   3/4   27/8      .       .         |    0     0  -3/4    27/8      .       .         0    0  1/16  27/16  81/16       .         |    0     0  1/16  -27/16  81/16       .         0    0     0   9/32   27/8  243/32         |    0     0     0    9/32  -27/8  243/32 But Gottfried, you didnt use the translation! For applying the regular iteration you have to *move* the fixed point to zero. The function graph is just translated so that the fixed point is situated at 0. No stretching or whatever is allowed. Here that would be $g_0(z)=(z-\frac{1}{4})^2+ (z-\frac{1}{4})-\frac{1}{16} + \frac{1}{4}=z^2-2\frac{1}{4}z+\frac{1}{16}+z-\frac{1}{4}-\frac{1}{16}+\frac{1}{4}=z^2+\frac{1}{2}z$ $g_1(z)=(z+\frac{1}{4})^2+(z+\frac{1}{4})-\frac{1}{16} - \frac{1}{4} = z^2+2\frac{1}{4}z+\frac{1}{16}+z+\frac{1}{4}-\frac{1}{16}-\frac{1}{4}=z^2+\frac{3}{2}z$ This is because regular half iteration is characterized as *the* half iteration that has at the fixed point $a$ the slope $f'(a)^{1/2}$. If you change the slope at the fixed point by the transformation, and you do by your transformation $g_1'(0)=(-\frac{1}{4}z^2+\frac{3}{2}z)'|_{z=0}=\frac{3}{2}\neq\frac{1}{2}=(2z+1)|_{z=-\frac{1}{4}}=f'(-\frac{1}{4})$, it is no more *regular* half iteration. « Next Oldest | Next Newest »

 Messages In This Thread the inconsistency depending on fixpoint-selection - by Gottfried - 02/07/2008, 03:06 PM RE: the inconsistency depending on fixpoint-selection - by Gottfried - 02/07/2008, 05:20 PM RE: the inconsistency depending on fixpoint-selection - by bo198214 - 03/04/2008, 10:14 AM RE: the inconsistency depending on fixpoint-selection - by bo198214 - 03/04/2008, 11:17 AM RE: the inconsistency depending on fixpoint-selection - by Gottfried - 03/04/2008, 11:25 AM RE: the inconsistency depending on fixpoint-selection - by Gottfried - 03/04/2008, 11:32 AM RE: the inconsistency depending on fixpoint-selection - by bo198214 - 03/04/2008, 11:43 AM RE: the inconsistency depending on fixpoint-selection - by GFR - 02/07/2008, 09:02 PM RE: the inconsistency depending on fixpoint-selection - by Gottfried - 02/07/2008, 09:49 PM RE: the inconsistency depending on fixpoint-selection - by Gottfried - 03/03/2008, 11:20 AM RE: the inconsistency depending on fixpoint-selection - by Gottfried - 03/06/2008, 04:06 PM RE: the inconsistency depending on fixpoint-selection - by bo198214 - 03/06/2008, 04:58 PM RE: the inconsistency depending on fixpoint-selection - by Gottfried - 03/06/2008, 05:25 PM RE: the inconsistency depending on fixpoint-selection - by Gottfried - 03/07/2008, 03:16 AM RE: the inconsistency depending on fixpoint-selection - by bo198214 - 03/07/2008, 10:56 AM RE: the inconsistency depending on fixpoint-selection - by Gottfried - 03/07/2008, 07:17 PM RE: the inconsistency depending on fixpoint-selection - by bo198214 - 03/07/2008, 08:30 PM RE: the inconsistency depending on fixpoint-selection - by Gottfried - 03/07/2008, 09:38 PM RE: the inconsistency depending on fixpoint-selection - by Gottfried - 03/08/2008, 01:22 PM RE: the inconsistency depending on fixpoint-selection - by Gottfried - 03/08/2008, 01:52 PM RE: the inconsistency depending on fixpoint-selection - by Gottfried - 03/08/2008, 04:21 PM RE: the inconsistency depending on fixpoint-selection - by bo198214 - 03/09/2008, 09:30 PM RE: the inconsistency depending on fixpoint-selection - by Gottfried - 03/14/2008, 02:10 PM RE: the inconsistency depending on fixpoint-selection - by Gottfried - 03/14/2008, 04:41 PM RE: the inconsistency depending on fixpoint-selection - by Gottfried - 03/14/2008, 07:19 PM RE: the inconsistency depending on fixpoint-selection - by bo198214 - 04/29/2008, 08:15 AM

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