A review of the numerical analysis of Golden split dichotomy

I've been reading it for 2012 years. The numerical discussion on the dichotomy of the Golden section, the reasoning formula does not remember, when the writing is not meticulous, the evening reviewed the next, did some supplementary

Original:

http://blog.csdn.net/aaajj/article/details/7878480

For example, ABCDE 5 nodes, organized by the following Fibonacci sequence two-way.

It takes 3 times to find a, which is the path from 5 onwards to a

It takes 3 times to find B.

It takes 2 times to find C

It takes 2 times to find D.

It takes 2 times to find E

Average expected e= total number of times/nodes = (3+3+2+2+2)/5 = 2.4

Here, set the Fibonacci sequence TN to 1 1 2 3 5 8 13 21 ...

Total number of sets is F

It can be found that, with the increase of the level, there is a recursive relationship

F0 = 0

F1 = 0

F2 = F1 + t (2) + F0 + t (1)

Fn = Fn-1 + t (N) + Fn-2 + t (n-1)

En = Fn/sum

= fn/t (n+1)

= (Fn-1 + Fn-2 + t (n+1))/t (n+1)

= 1 + Fn-1/t (n+1) + Fn-2/t (n+1)

= 1 + En-1 * t (n)/t (n+1) + En-2 *t (n-1)

As can be seen from here, the expectation is exactly 2 blocks of the expected value plus the depth of 1, in the mathematical calculation and the logic is also consistent

The numerical analysis program and data are shown in the original

http://blog.csdn.net/aaajj/article/details/7878480

A review of the numerical analysis of Golden split dichotomy