Let A be a given positive constant and g(x)=2x-Ax^2 a. Show that if fixed-point iteration converges to a nonzero limit, then the limit is p=1/A, so the reciprocal of a number can be found using only multiplications and subtractions b. Find an interval about 1/A for which fixed-point iteration converges, provided p0 is in the interval Can any one help with this problem
The condition for a fixed point is g(p) =p By substitution if p =1/A g(1/A) = 2/A - A(1/A^2) = 1/A(2 - 1) = 1/A as required.