# Numerical analysis problem

#### tedeman

Joined May 12, 2008
2
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

#### studiot

Joined Nov 9, 2007
5,003
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.

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