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+--- Thread: correct derivatives wrt iteration height? (/showthread.php?tid=238)
correct derivatives wrt iteration height? - Gottfried - 02/20/2009
Hi
I never followed the discussions about derivatives/integrals (it was all much enough with that what I had to follow... :-) )
Now I'm trying to step into that field, first trying to re-express the derivatives wrt to the height-parameter in terms of my matrix-language.
Could someone crosscheck, whether these values match the "official" values?
Code:
Table of derivatives wrt iteration-height h of f°h(x): df°h(x)/dh
using f(x) = 2^x - 1
First derivatives at few different heights and x.
At h=0 I have also computed the second derivatives.
------------------------------------------------------------------
h=0.1 h=0 h=-0.5 h=-1
------------------------------------------------------------------
x=1.5 0.2478643 0.2332798 0.17517130 0.13462
0.13462
------------------------------------------------------------------
x=1 0 0 0 0
0
------------------------------------------------------------------
x=0.5 0.0862732 0.0862134 0.08516093 -0.08291
-0.08291
------------------------------------------------------------------
x=0 0 0 0 0
0
------------------------------------------------------------------
x=-0.5 0.2715139 0.2945423 0.46660375 0.849869
-0.244133
------------------------------------------------------------------
x=-1 0.7414847 0.8498694 2.14011104 ???
-1.205064
------------------------------------------------------------------
x=-2 2.3070256 3.0900585 ??? ???
-10.03082
------------------------------------------------------------------Gottfried