Minimum of a Function Using the Fibonacci Sequence

Consider the function

f(x)=

2

x

-sin(sx)

,

0<x<1

, where

s

is a parameter. This Demonstration approximates the minimum of

f

using an algorithm based on the Fibonacci sequence, shown by a magenta point on the plot of

f(x)

. For comparison, the blue point is the minimum found by Mathematica's built-in function NMinimize. When

ϵ

is sufficiently small, there is good agreement.

You can vary the values of

s

and

ϵ

(see the Details section for the definition of

ϵ

). The Demonstration plots

f(x)

and you can see a table of points in the iteration of the algorithm.