🚀 go-pugleaf

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.

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.


They are also useful in the design of sunflowers and pine-cones.
 
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