🚀 go-pugleaf

Dr John Stockton heeft geschreven in bericht ...
>JRS:  In article <8g1qgd$bmh$1@news.IAEhv.nl> of Fri, 19 May
2000
>00:36:45 seen in news:comp.lang.pascal.borland, Huub van Dooren
><hvdooren@iae.nl> wrote:
>>>Argh! That has to be the absolutely worst example for
recursion.
>>It
>>>takes exponential time to solve a linear problem when one uses
>>>recursion with Fibonacci numbers.
>>>
>>
>>You're right. Bad example. But almost every textbook uses this
>>as an introduction to (the problems of using) recursion. BTW
>>I never found any use for them in all of programs anyhow.  ;-)
>
>
>They are useful if you have a function known to have a single
maximum
>(and no minima) within a given range, and you wish to locate
that
>maximum to within a predefined accuracy while using the minimum
number
>of function evaluations.
>

Is this a parabolic function, or what? Or are there relative
maxima near the
absolute maximum. Or is it a compound (is that the right word?)
function?

>At each step, you are considering two evaluated points within
the
>remaining range, dividing the range into three, and the maximum
cannot
>lie between the smaller and its nearer end-of-range.
>
>The larger point is reused in the next step, and Fibonacci-based
>positioning ensures that each step reduces the range as much as
>possible.  In the final step, the points are at 1/3 & 2/3 of
possible
>range.
>

Never had Fibonacci-based successive substitution at school. I
only had
Riemann-suc-sub and Newton-Raphson-method. As I do recall (about
15 years ago, now), the convergency to the maximum, is reached
much
faster by using f'(x) to determine the next step.
>
>They are also useful in the design of sunflowers and pine-cones.
>

Tell my about the pine-cones and I will tell you about the
rabbits. 8-)


Greetings. Huub.