Iteration exercises: f(x)=x^2 - 0.5 ; Fixpoint-irritation...

[Gottfried]

in particular i do not understand your matrix idea in this thread.

You may look at alternating sum of iterates (here: of exponential function) There I describe the method first time however with another function as basis: the exponential function.

The problem of convergence of series of matrices surfaces, and the question of convergence of the shortcutformula for the geometric series especially.

Nearly everything was completely new for me, so this article should be rewritten; anyway in its naivety it might be a good introductory impulse to understand the key idea for that matrix-method and possibly engage in the area which I call now "iteration-series" in resemblance to "powerseries" and "dirichletseries".

Gottfried