1. Fixed-Point Iteration
Theorem 1.3 (Fixed-Point Theorem). Assume that g(x) and g’(x) are continuous on a balanced interval (a,b) = that contains the unique fixed point P and that the starting value p0 is chosen in this interval.
If for all , then the iteration pn = g(pn-1) will converge to P. In this case P is an attractive fixed point.