Minimum of a Function Using the Fibonacci Sequence
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.
f(x)=-sin(sx)
2
x
0<x<1
s
f
f(x)
ϵ
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.
s
ϵ
ϵ
f(x)