Minimum of a Function Using the Fibonacci Sequence
Consider the function , , where is a parameter. This Demonstration approximates the minimum of using an algorithm based on the Fibonacci sequence, shown by a magenta point on the plot of . For comparison, the blue point is the minimum found by Mathematica's built-in function NMinimize. When is sufficiently small, there is good agreement.[more]
You can vary the values of and (see the Details section for the definition of ). The Demonstration plots and you can see a table of points in the iteration of the algorithm.[less]
Steps involved in a Fibonacci search:
1. Calculate , where is the interval in which is defined.
2. Identify such that where is the Fibonacci sequence.
3. Set and .
4. Calculate and .
5. If , set and ; otherwise set and .
6. Set and go to step 3.
7. Stop when .
 J. H. Mathews. "Module for the Fibonacci Search." (Apr 30, 2013) mathfaculty.fullerton.edu/mathews/n2003/FibonacciSearchMod.html.