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

Helmut Knaust, Department of Mathematical Sciences, UTEP, El Paso TX 79968
hknaust@utep.edu
9/23/2003; last edit 8/21/2020

Every time you open a notebook, you need to evaluate the command (s) containing ":=" first.
To evaluate a command, click on the cell bracket on the right adjacent to the command, then hit ⇧ and ⌤ simultaneously.

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_,n_,x0_]:=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,-2.3,100,0.4]

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[0.8,2.313,80,114.7]