Math 2325
Project 1 (Chapter 1) - Iteration of Linear Functions

Iterations

The following command produces a list of the first niterations of the function  f(x)=a x+b with initial value (Subscript[x, 0]).

Iteration[a_,b_,x0_,n_]:=NestList[Function[x,a x+b],x0,n]

Here is an example: f(x)=1.1x-2.3, initial value (Subscript[x, 0])=0.4, 100 iterations. The sequence of iterations seems to diverge.

Iteration[1.1,-2.3,0.4,100]

Here are the first 80 iterations of the function f(x)=0.8 x+2.313 with initial value (Subscript[x, 0])=114.7. The sequence of iterations seems to converge.

Iteration[0.8,2.313,114.7, 80]

Helmut Knaust, hknaust@utep.edu.	
September 23, 2003.

slight updates: Art Duval, artduval@math.utep.edu
September 3, 2008.