A guide to Fixed Point lab

Purpose

The purpose with Fixed Point lab is to illustrate what is a "fixed point" and what is "fixed point iteration", related to equations of the form x=g(x).

What you can do

1. Give the function g(x) involved in the equation x = g(x) under consideration, or select an example one from the popup menu.
2. View the solution(s) (intersection(s) of y = x and y = g(x)) of the given equation x = g(x) in the graph window.
3. Zoom in or out to get a better of more complete view if desired.
4. Give an x-value and get an evaluation of the corresponding g(x). If very lucky you find that g(x) = x.
5. Use the idea of "fixed point iteration" by (repeatedly) use the current g(x)-value to redefine x as x_new = g(x_current), followed by the obvious redefinition u_current = u_new.
6. Automize this iteration process by repeatedly (until g(x) does not significantly differ from the input x) pressing the iterate button, or giving a certain number of iterations in the "nits =" text edit box, or ask for iterations until a certain error tolerance has been reached by defining a desired tolerance in the "tol =" text edit box.

How to do it

1. To give a function g(x), simply type the desired g(x) formula in the "g(x) =" text edit box, followed by a return. Recall that the given g(x) formula should be a valid matlab expression, allowed to depend on the varaible x.
2. To pick an example g(x) function, use the popupmenu below the "g(x) =" text edit box.
3. To zoom, in or out, press the desired zoom button and then click at the desired center point in the new zoomed plot in the plot window.
4. To give an x-value and get the corresponding g(x)-value computed, simply type the x-value in the "x =" text edit box followed by a return.
5. To fixed point iterate "manually", simply give the current g(x)-value as a new x-value, and give a return to reevaluate the resulting new g(x)- value.
6. To automize the iteration, repeatedly press the "iterate" button, or give a desired number of iteration steps in the "nits =" text edit box,

Problems

1.